Existence results for some anisotropic elliptic problems having variable exponent and \(L^1\)-data

DOI10.15407/MAG19.04.696MaRDI QIDQ6493799

Hassane Hjiaj, Mohamed Badr Benboubker

Publication date: 29 April 2024

Published in: Journal of Mathematical Physics, Analysis, Geometry (Search for Journal in Brave)

zbMATH Keywords

Sobolev spacesnonlinear elliptic problementropy solutionsvariable exponentanisotropicpenalization techniques

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Strong solutions to PDEs (35D35)

Cites Work

• Existence of solutions for a class of obstacle problems with \(L^1\)-data and without sign condition
• Existence of solutions in the sense of distributions of anisotropic nonlinear elliptic equations with variable exponent
• Lebesgue and Sobolev spaces with variable exponents
• Nonlinear elliptic equations in \(\mathbb{R}^ N\) without growth restrictions on the data
• Sobolev inequalities with variable exponent attaining the values 1 and \(n\)
• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• On some \(p(x)\)-quasilinear problem with right-hand side measure
• Entropy and renormalized solutions for nonlinear elliptic problem involving variable exponent and measure data
• An approximation result in generalized anisotropic Sobolev spaces and applications
• Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent
• Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
• Entropy solutions for the $p(x)$-Laplace equation
• Strongly nonlinear elliptic equations having natural growth terms and L1 data
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)

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