Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"The hydrostatic approximation of the Boussinesq equations with rotation in a thin domain","authors":"Xueke Pu ,&nbsp;Wenli Zhou","doi":"10.1016/j.na.2024.113688","DOIUrl":"10.1016/j.na.2024.113688","url":null,"abstract":"<div><div>In this paper, the global existence of strong solutions to the primitive equations with only horizontal viscosity and diffusivity is established under the assumption of initial data <span><math><mrow><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> with additional regularity <span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>z</mi></mrow></msub><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math></span>. Moreover, we prove that the scaled Boussinesq equations with rotation strongly converge to the primitive equations with only horizontal viscosity and diffusivity, with the convergence rate <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>λ</mi></mrow><mrow><mo>min</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mi>β</mi><mo>−</mo><mn>2</mn><mo>,</mo><mi>γ</mi><mo>−</mo><mn>2</mn><mo>}</mo></mrow><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mo>&lt;</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>&lt;</mo><mi>∞</mi><mo>)</mo></mrow></mrow></math></span>, in the cases of initial data <span><math><mrow><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> with <span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>z</mi></mrow></msub><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></mrow></math></span> and initial data <span><math><mrow><mrow><mo>(</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, respectively, as the aspect ratio <span><math><mi>λ</mi></math></span> goes to zero.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113688"},"PeriodicalIF":1.3,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142571407","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":"Partial gradient regularity for parabolic systems with degenerate diffusion and Hölder continuous coefficients","authors":"Fabian Bäuerlein","doi":"10.1016/j.na.2024.113691","DOIUrl":"10.1016/j.na.2024.113691","url":null,"abstract":"<div><div>We consider vector valued weak solutions <span><math><mrow><mi>u</mi><mo>:</mo><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> with <span><math><mrow><mi>N</mi><mo>∈</mo><mi>N</mi></mrow></math></span> of degenerate or singular parabolic systems of type <span><span><span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>−</mo><mi>div</mi><mspace></mspace><mi>a</mi><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>D</mi><mi>u</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mspace></mspace><mtext>in</mtext><mspace></mspace><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>=</mo><mi>Ω</mi><mo>×</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>where <span><math><mi>Ω</mi></math></span> denotes an open set in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> for <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>T</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> a finite time. Assuming that the vector field <span><math><mi>a</mi></math></span> is not of Uhlenbeck-type structure, satisfies <span><math><mi>p</mi></math></span>-growth assumptions and <span><math><mrow><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>↦</mo><mi>a</mi><mrow><mo>(</mo><mi>z</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></mrow></mrow></math></span> is Hölder continuous for every <span><math><mrow><mi>ξ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi><mi>n</mi></mrow></msup></mrow></math></span>, we show that the gradient <span><math><mrow><mi>D</mi><mi>u</mi></mrow></math></span> is partially Hölder continuous, provided the vector field degenerates like that of the <span><math><mi>p</mi></math></span>-Laplacian for small gradients.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113691"},"PeriodicalIF":1.3,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gap results and existence of free boundary CMC surfaces in rotational domains","authors":"Allan Freitas ,&nbsp;Márcio S. Santos ,&nbsp;Joyce S. Sindeaux","doi":"10.1016/j.na.2024.113681","DOIUrl":"10.1016/j.na.2024.113681","url":null,"abstract":"<div><div>In this paper, we work with the existence and uniqueness of free boundary constant mean curvature surfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. We classify the free boundary CMC surfaces as topological disks or annulus under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor. Also, we construct some examples of free boundary CMC surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113681"},"PeriodicalIF":1.3,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142554046","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":"Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction","authors":"Mónica Clapp ,&nbsp;Víctor Hernández-Santamaría ,&nbsp;Alberto Saldaña","doi":"10.1016/j.na.2024.113680","DOIUrl":"10.1016/j.na.2024.113680","url":null,"abstract":"<div><div>We study the existence and concentration of positive and nodal solutions to a Schrödinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suitable rescaling, the concentration gives rise to a limiting profile that solves a nonautonomous elliptic semilinear equation with a sharp sign change in the nonlinearity. We characterize the (radial or foliated Schwarz) symmetries and the (polynomial) decay of the least-energy positive and nodal limiting profiles.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113680"},"PeriodicalIF":1.3,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Precise asymptotics near a generic S1×R3 singularity of mean curvature flow","authors":"Zhou Gang ,&nbsp;Shengwen Wang","doi":"10.1016/j.na.2024.113679","DOIUrl":"10.1016/j.na.2024.113679","url":null,"abstract":"<div><div>In the present paper we study a type of generic singularity of mean curvature flow modelled on the bubble-sheet <span><math><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>, and we derive an asymptotic profile for a neighbourhood of singularity.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113679"},"PeriodicalIF":1.3,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermostatted kinetic theory in measure spaces: Well-posedness","authors":"Carlo Bianca ,&nbsp;Nicolas Saintier","doi":"10.1016/j.na.2024.113666","DOIUrl":"10.1016/j.na.2024.113666","url":null,"abstract":"<div><div>This paper is devoted to the generalization of the thermostatted kinetic theory within the framework of probability measures. Specifically well-posedness of the Cauchy problem related to a thermostatted kinetic equation for measure-valued functions is established. The external force applied to the system is assumed to be Lipschitz, in contrast to previous work where external forces are generally constant. Existence is obtained by employing an Euler-like approximation scheme which is shown to converge assuming the initial condition has moment of order greater than 2. Uniqueness is proved assuming the gain operator is Lipschitz w.r.t a (new) Monge–Kantorovich–Wasserstein distance <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn><mo>−</mo></mrow></msub></math></span>, intermediate between the classical <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>W</mi></mrow><mrow><mi>r</mi></mrow></msub></math></span>, <span><math><mrow><mi>r</mi><mo>&lt;</mo><mn>2</mn></mrow></math></span>, distances. The assumptions on the gain operator are quite general covering <span><math><mi>n</mi></math></span>-ary interaction, and apply in particular to the Kac equation.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113666"},"PeriodicalIF":1.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425203","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":"Positive solutions for a Kirchhoff problem of Brezis–Nirenberg type in dimension four","authors":"Giovanni Anello,&nbsp;Luca Vilasi","doi":"10.1016/j.na.2024.113675","DOIUrl":"10.1016/j.na.2024.113675","url":null,"abstract":"<div><div>We consider a Kirchhoff problem of Brezis–Nirenberg type in a smooth bounded domain of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> with Dirichlet boundary conditions. Our approach, novel in this framework and based upon approximation arguments, allows us to cope with the interaction between the higher order Kirchhoff term and the critical nonlinearity, typical of the dimension four. We derive several existence results of positive solutions, complementing and improving earlier results in the literature. In particular, we provide explicit bounds of the parameters <span><math><mi>b</mi></math></span> and <span><math><mi>λ</mi></math></span> coupled, respectively, with the higher order Kirchhoff term and the subcritical nonlinearity, for which the existence of solutions occurs.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113675"},"PeriodicalIF":1.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425252","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":"Minimization of Dirichlet energy of j−degree mappings between annuli","authors":"David Kalaj","doi":"10.1016/j.na.2024.113671","DOIUrl":"10.1016/j.na.2024.113671","url":null,"abstract":"<div><div>Let <span><math><mi>A</mi></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∗</mo></mrow></msub></math></span> be circular annuli in the complex plane, and consider the Dirichlet energy integral of <span><math><mi>j</mi></math></span>-degree mappings between <span><math><mi>A</mi></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∗</mo></mrow></msub></math></span>. We aim to minimize this energy integral. The minimizer is a <span><math><mi>j</mi></math></span>-degree harmonic mapping between the annuli <span><math><mi>A</mi></math></span> and <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∗</mo></mrow></msub></math></span>, provided it exists. If such a harmonic mapping does not exist, then the minimizer is still a <span><math><mi>j</mi></math></span>-degree mapping which is harmonic in <span><math><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>⊂</mo><mi>A</mi></mrow></math></span>, and it is a squeezing mapping in its complementary annulus <span><math><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup><mo>=</mo><mi>A</mi><mo>∖</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math></span>. This result is an extension of a certain result by Astala et al. (2010).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113671"},"PeriodicalIF":1.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425202","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":"Asymmetric affine Poincaré–Sobolev–Wirtinger inequalities on BV(Ω) and characterization of extremizers in one-dimension","authors":"Raul Fernandes Horta,&nbsp;Marcos Montenegro","doi":"10.1016/j.na.2024.113673","DOIUrl":"10.1016/j.na.2024.113673","url":null,"abstract":"<div><div>The present work deals with sharp asymmetric Poincaré–Sobolev–Wirtinger inequalities involving the Zhang’s energy on the space of bounded variation functions <span><math><mrow><mi>B</mi><mi>V</mi><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> for any bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> in any dimension <span><math><mrow><mi>n</mi><mo>≥</mo><mn>1</mn></mrow></math></span>. We establish the existence of a curve of optimal constants along with several of its properties such as attainability, symmetry, monotonicity, positivity, continuity and also asymptotic ones. Moreover, for <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>, our approach allows to exhibit its precise shape and to characterize all extremizers.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113673"},"PeriodicalIF":1.3,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425251","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 asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1","authors":"Giovany M. Figueiredo ,&nbsp;Marcos T.O. Pimenta ,&nbsp;Patrick Winkert","doi":"10.1016/j.na.2024.113677","DOIUrl":"10.1016/j.na.2024.113677","url":null,"abstract":"<div><div>In this paper we study the asymptotic behavior of solutions to the <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-equation <span><span><span><math><mrow><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>q</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace><mtext>on</mtext><mi>∂</mi><mi>Ω</mi><mo>,</mo></mrow></math></span></span></span>as <span><math><mrow><mi>p</mi><mo>→</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span>, where <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>&lt;</mo><mi>q</mi><mo>&lt;</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>∗</mo></mrow></msup><mo>≔</mo><mi>N</mi><mo>/</mo><mrow><mo>(</mo><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and <span><math><mi>f</mi></math></span> is a Carathéodory function that grows superlinearly and subcritically. Based on a Nehari manifold treatment, we are able to prove that the <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplace problem given by <span><span><span><math><mrow><mo>−</mo><mo>div</mo><mfenced><mrow><mfrac><mrow><mo>∇</mo><mi>u</mi></mrow><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow></mfrac></mrow></mfenced><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>q</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace><mtext>on</mtext><mi>∂</mi><mi>Ω</mi><mo>,</mo></mrow></math></span></span></span>has at least two constant sign solutions and one sign-changing solution, whereby the sign-changing solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space <span><math><mrow><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mi>q</mi></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space <span><math><mrow><mo>BV</mo><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> of all functions of bounded variation. As far as we know this is the first work dealing with <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-Laplace problems even in the direction of constant sign solutions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"251 ","pages":"Article 113677"},"PeriodicalIF":1.3,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142425249","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}