Nonlinear Analysis-Theory Methods & Applications最新文献

{"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":"The non-convex planar least gradient problem","authors":"Samer Dweik ,&nbsp;Piotr Rybka ,&nbsp;Ahmad Sabra","doi":"10.1016/j.na.2025.113843","DOIUrl":"10.1016/j.na.2025.113843","url":null,"abstract":"<div><div>We study the least gradient problem in bounded regions with Lipschitz boundary in the plane. We provide a set of conditions for the existence of solutions in non-convex simply connected regions. We assume the boundary data is continuous and in the space of functions of bounded variation, and we are interested in solutions that satisfy the boundary conditions in the trace sense. Our method relies on the equivalence of the least gradient problem and the Beckmann problem which allows us to use the tools of the optimal transportation theory.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113843"},"PeriodicalIF":1.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107023","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":"Marcinkiewicz-type multiplier theorem for multi-parameter paraproducts","authors":"Yaryong Heo ,&nbsp;Sunggeum Hong ,&nbsp;Chan Woo Yang","doi":"10.1016/j.na.2025.113832","DOIUrl":"10.1016/j.na.2025.113832","url":null,"abstract":"<div><div>In this paper, we establish Marcinkiewicz-type multiplier theorems for multi-linear and multi-parameter Fourier multiplier operators. For <span><math><mi>n</mi></math></span>-linear and multi-parameter Fourier multiplier operators, Muscalu et al. (2004,2006) obtained <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><mo>×</mo><mo>⋯</mo><mo>×</mo><msup><mrow><mi>L</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msup><mo>→</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></mrow></math></span> estimates for all <span><math><mrow><mn>1</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>&lt;</mo><mi>∞</mi></mrow></math></span> and <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span>, under the condition that <span><math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>+</mo><mo>⋯</mo><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfrac></mrow></math></span>. Their approach assumed that the multipliers and their derivatives satisfy specific pointwise estimates (the Mihlin-type condition). In contrast, we will consider multi-linear and multi-parameter operators whose multipliers exhibit limited smoothness, characterized by a function space rather than pointwise conditions (the Marcinkiewicz-type condition). The Marcinkiewicz-type multiplier condition addressed in this paper involves the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-average of the multiplier and its derivatives. This approach allows us to address a wider variety of multipliers compared to the Mihlin-type condition.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113832"},"PeriodicalIF":1.3,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144083965","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}

{"title":"A game interpretation for the weighted p-Laplace equation","authors":"Mamoru Aihara","doi":"10.1016/j.na.2025.113829","DOIUrl":"10.1016/j.na.2025.113829","url":null,"abstract":"<div><div>In this paper, we obtain a stochastic approximation that converges to the viscosity solution of the weighted <span><math><mi>p</mi></math></span>-Laplace equation. We consider a stochastic two-player zero-sum game controlled by a random walk, two player’s choices, and the gradient of the weight function. The proof is based on the boundary conditions in the viscosity sense and the comparison principle. These results extend previous findings for the non-weighted <span><math><mi>p</mi></math></span>-Laplace equation (Manfredi et al., 2012). In addition, we study the limiting behavior of the viscosity solution of the weighted <span><math><mi>p</mi></math></span>-Laplace equation as <span><math><mrow><mi>p</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"259 ","pages":"Article 113829"},"PeriodicalIF":1.3,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904208","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}