Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"De Leeuw representations of functionals on Lipschitz spaces","authors":"Ramón J. Aliaga , Eva Pernecká , Richard J. Smith","doi":"10.1016/j.na.2025.113851","DOIUrl":"10.1016/j.na.2025.113851","url":null,"abstract":"<div><div>Let <span><math><mrow><msub><mrow><mi>Lip</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> be the space of Lipschitz functions on a complete metric space <span><math><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>d</mi><mo>)</mo></mrow></math></span> that vanish at a point <span><math><mrow><mn>0</mn><mo>∈</mo><mi>M</mi></mrow></math></span>. We investigate its dual <span><math><mrow><msub><mrow><mi>Lip</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> using the De Leeuw transform, which allows representing each functional on <span><math><mrow><msub><mrow><mi>Lip</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span> as a (non-unique) measure on <span><math><mrow><mi>β</mi><mover><mrow><mi>M</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow></math></span>, where <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> is the space of pairs <span><math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>∈</mo><mi>M</mi><mo>×</mo><mi>M</mi></mrow></math></span>, <span><math><mrow><mi>x</mi><mo>≠</mo><mi>y</mi></mrow></math></span>. We distinguish a set of points of <span><math><mrow><mi>β</mi><mover><mrow><mi>M</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow></math></span> that are “away from infinity”, which can be assigned coordinates belonging to the Lipschitz realcompactification <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msup></math></span> of <span><math><mi>M</mi></math></span>. We define a natural metric <span><math><mover><mrow><mi>d</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> on <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msup></math></span> extending <span><math><mi>d</mi></math></span> and we show that optimal (i.e. positive and norm-minimal) De Leeuw representations of well-behaved functionals are characterised by <span><math><mover><mrow><mi>d</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-cyclical monotonicity of their support, extending known results for functionals in <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span>, the predual of <span><math><mrow><msub><mrow><mi>Lip</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow></math></span>. We also extend the Kantorovich–Rubinstein theorem to normal Hausdorff spaces, in particular to <span><math><msup><mrow><mi>M</mi></mrow><mrow><mi>R</mi></mrow></msup></math></span>, and use this to characterise measure-induced and majorisable functionals in <span><math><mrow><msub><mrow><mi>Lip</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mrow><mo>(</mo><mi>M</mi><mo>)</mo></mrow></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> as those admitting optimal representations ","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113851"},"PeriodicalIF":1.3,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BMO estimates for Hodge–Maxwell systems with discontinuous anisotropic coefficients","authors":"Dharmendra Kumar ,&nbsp;Swarnendu Sil","doi":"10.1016/j.na.2025.113852","DOIUrl":"10.1016/j.na.2025.113852","url":null,"abstract":"<div><div>We prove up to the boundary <span><math><mi>BMO</mi></math></span> estimates for linear Maxwell–Hodge type systems for <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>-valued differential <span><math><mi>k</mi></math></span>-forms <span><math><mi>u</mi></math></span> in <span><math><mi>n</mi></math></span> dimensions <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mi>d</mi></mrow><mrow><mo>∗</mo></mrow></msup><mfenced><mrow><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>d</mi><mi>u</mi></mrow></mfenced></mtd><mtd><mo>=</mo><mi>f</mi></mtd><mtd></mtd><mtd><mtext>in</mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mi>d</mi></mrow><mrow><mo>∗</mo></mrow></msup><mfenced><mrow><mi>B</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi></mrow></mfenced></mtd><mtd><mo>=</mo><mi>g</mi></mtd><mtd></mtd><mtd><mtext>in</mtext><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>with <span><math><mrow><mi>ν</mi><mo>∧</mo><mi>u</mi></mrow></math></span> prescribed on <span><math><mrow><mi>∂</mi><mi>Ω</mi><mo>,</mo></mrow></math></span> where the coefficient tensors <span><math><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></math></span> are only required to be bounded measurable and in a class of ‘small multipliers of BMO’. This class neither contains nor is contained in <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>.</mo></mrow></math></span> Since the coefficients are allowed to be discontinuous, the usual Korn’s freezing trick cannot be applied. As an application, we show BMO estimates hold for the time-harmonic Maxwell system in dimension three for a class of discontinuous anisotropic permeability and permittivity tensors. The regularity assumption on the coefficient is essentially sharp.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113852"},"PeriodicalIF":1.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlocal approximation of an anisotropic cross-diffusion system","authors":"Tomasz Dębiec ,&nbsp;Markus Schmidtchen","doi":"10.1016/j.na.2025.113835","DOIUrl":"10.1016/j.na.2025.113835","url":null,"abstract":"<div><div>Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the nonlocal-to-limit for a specific anisotropic cross-diffusion system encountered in population dynamics featuring phase-separation phenomena, i.e., internal layers between different species. A critical element of the proof is an entropy dissipation identity, which we show to hold for any weak solution.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113835"},"PeriodicalIF":1.3,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chemotaxis-consumption interaction: Solvability and asymptotics in general high-dimensional domains","authors":"Johannes Lankeit ,&nbsp;Michael Winkler","doi":"10.1016/j.na.2025.113853","DOIUrl":"10.1016/j.na.2025.113853","url":null,"abstract":"<div><div>The basic chemotaxis-consumption model <span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>u</mi><mo>∇</mo><mi>v</mi><mo>)</mo></mrow><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi></mtd></mtr></mtable></mrow></mfenced></math></span> is considered in general, possibly non-convex bounded domains of arbitrary spatial dimension. Global existence of weak solutions is shown, along with eventual smoothness of solutions and their stabilization in the large time limit.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113853"},"PeriodicalIF":1.3,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144178693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Monge–Ampère equations with right-hand sides of polynomial growth","authors":"Beomjun Choi ,&nbsp;Kyeongsu Choi ,&nbsp;Soojung Kim","doi":"10.1016/j.na.2025.113849","DOIUrl":"10.1016/j.na.2025.113849","url":null,"abstract":"<div><div>We study the regularity and the growth rates of solutions to two-dimensional Monge–Ampère equations with the right-hand side exhibiting polynomial growth. Utilizing this analysis, we demonstrate that the translators for the flow by sub-affine-critical powers of the Gauss curvature are smooth, strictly convex entire graphs. These graphs exhibit specific growth rates that depend solely on the power of the flow.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113849"},"PeriodicalIF":1.3,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144154433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Triviality of k-Yamabe gradient solitons immersed in certain warped product spaces","authors":"Henrique F. de Lima,&nbsp;Ary V.F. Leite,&nbsp;Marco A.L. Velásquez","doi":"10.1016/j.na.2025.113848","DOIUrl":"10.1016/j.na.2025.113848","url":null,"abstract":"<div><div>We deal with complete noncompact and stochastically complete <span><math><mi>k</mi></math></span>-Yamabe gradient solitons immersed in a warped product space obeying a suitable curvature constraint. In this context, we establish a necessary and sufficient condition for a Riemannian manifold immersed in a warped product to be a <span><math><mi>k</mi></math></span>-Yamabe gradient soliton, under the hypothesis that the potential function agrees with the height function. Proceeding with this setting, we use a suitable Bochner type formula jointly with integrability conditions and some maximum principles dealing, in particular, with the notions of convergence to zero at infinity and polynomial volume growth, to obtain new triviality results concerning <span><math><mi>k</mi></math></span>-Yamabe gradient solitons. Moreover, we present some applications of our main results to a class of pseudo-hyperbolic spaces.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113848"},"PeriodicalIF":1.3,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normalized solutions to Schrödinger systems with critical nonlinearities","authors":"Yuxi Meng ,&nbsp;Xiaoming He ,&nbsp;Patrick Winkert","doi":"10.1016/j.na.2025.113845","DOIUrl":"10.1016/j.na.2025.113845","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We consider a system of coupled Schrödinger equations involving critical exponent given by &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mtext&gt;in&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;We study the existence of positive ground state solutions having prescribed mass &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mtext&gt;and&lt;/mtext&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mo&gt;∫&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;where &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;q&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;m","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113845"},"PeriodicalIF":1.3,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vanishing results on weighted manifolds with lower bounds of the curvature operator","authors":"Nguyen Thac Dung ,&nbsp;Juncheol Pyo ,&nbsp;Nguyen Dang Tuyen","doi":"10.1016/j.na.2025.113847","DOIUrl":"10.1016/j.na.2025.113847","url":null,"abstract":"<div><div>In this paper, we apply a new Bochner technique introduced in the recent work by Petersen and Wink to investigate vanishing properties of <span><math><mi>p</mi></math></span>-harmonic <span><math><mi>ℓ</mi></math></span>-forms on Riemannian manifolds. Assuming that <span><math><mi>M</mi></math></span> is a complete, noncompact <span><math><mi>n</mi></math></span>-dimensional manifold with an <span><math><mrow><mo>(</mo><mi>n</mi><mo>−</mo><mi>ℓ</mi><mo>)</mo></mrow></math></span>-positive curvature operator, we demonstrate that any <span><math><mi>p</mi></math></span>-harmonic <span><math><mi>ℓ</mi></math></span>-forms on <span><math><mi>M</mi></math></span> with finite <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>-energy must be trivial. To establish this result, we consider a general framework for a complete noncompact weighted Riemannian manifold <span><math><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>f</mi></mrow></msup><mi>d</mi><mi>μ</mi><mo>)</mo></mrow></math></span> where the weighted curvature operator is bounded from below. By assuming the validity of a Sobolev inequality on <span><math><mrow><mo>(</mo><mi>M</mi><mo>,</mo><mi>g</mi><mo>,</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>f</mi></mrow></msup><mi>d</mi><mi>μ</mi><mo>)</mo></mrow></math></span>, we apply the Moser iteration technique to estimate the sup-norm of forms and verify their vanishing properties.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113847"},"PeriodicalIF":1.3,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144072351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A priori estimates for Singularities of the Lagrangian Mean Curvature Flow with supercritical phase","authors":"Arunima Bhattacharya,&nbsp;Jeremy Wall","doi":"10.1016/j.na.2025.113844","DOIUrl":"10.1016/j.na.2025.113844","url":null,"abstract":"<div><div>In this paper, we prove interior a priori estimates for singularities of the Lagrangian mean curvature flow assuming the Lagrangian phase is supercritical. We prove a Jacobi inequality that holds good when the Lagrangian phase is critical and supercritical. We further extend our results to a broader class of Lagrangian mean curvature type equations.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113844"},"PeriodicalIF":1.3,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence results for some elliptic problems in RN including variable exponents above the critical growth","authors":"Yane Araújo ,&nbsp;Eudes Barboza ,&nbsp;José Carlos de Albuquerque ,&nbsp;Pedro Ubilla","doi":"10.1016/j.na.2025.113831","DOIUrl":"10.1016/j.na.2025.113831","url":null,"abstract":"<div><div>We establish existence results for the following class of equations involving variable exponents <span><span><span><math><mrow><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mrow><mo>(</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>)</mo></mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><mi>λ</mi><msup><mrow><mrow><mo>|</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>|</mo></mrow></mrow><mrow><mi>q</mi><mrow><mo>(</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>)</mo></mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>λ</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math></span> and <span><math><mrow><mi>p</mi><mo>,</mo><mi>q</mi><mo>:</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mi>∞</mi><mo>)</mo></mrow><mo>→</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mo>+</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span> are radial continuous functions which satisfy suitable conditions. For this purpose, it is sufficient to consider either subcriticality or criticality within a small region near the origin. Surprisingly, outside this region, the nonlinearity may oscillate between subcritical, critical, and supercritical growth in the Sobolev sense. Our approach enables the use of the variational methods to tackle problems with variable exponents in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> without imposing restrictions outside of a neighborhood of zero.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113831"},"PeriodicalIF":1.3,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143927393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}