Compact embedding from \(W_0^{1,2}(\Omega)\) to \(L^{q(x)}(\Omega )\) and its application to nonlinear elliptic boundary value problem with variable critical exponent

DOI10.1016/j.jmaa.2007.07.083zbMath1151.46020OpenAlexW2045406361MaRDI QIDQ2465894

Kazuhiro Kurata, Naoki Shioji

Publication date: 10 January 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.07.083

zbMATH Keywords

Sobolev spacescompact embeddingvariable exponentnonlinear elliptic boundary value problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Equations involving nonlinear operators (general) (47J05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (15)

Strauss's radial compactness and nonlinear elliptic equation involving a variable critical exponent ⋮ Infinitely many sign-changing solutions for a semilinear elliptic equation with variable exponent ⋮ Compact embeddings for Sobolev spaces of two variable exponents ⋮ Almost compact and compact embeddings of variable exponent spaces ⋮ Doubly nonlinear parabolic equations involving variable exponents ⋮ Sobolev inequalities for Musielak-Orlicz spaces ⋮ Existence of nontrivial radial solution for semilinear equation with critical or supercritical variable exponent ⋮ Infinitely many small solutions for the \( p (x)\)-Laplacian operator with nonlinear boundary conditions ⋮ Sobolev's inequality for Musielak-Orlicz-Sobolev functions ⋮ SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS ⋮ Sign-changing solutions for semilinear elliptic equation with variable exponent ⋮ Subdifferential calculus and doubly nonlinear evolution equations in \(L^p\)-spaces with variable exponents ⋮ Overview of differential equations with non-standard growth ⋮ Unnamed Item ⋮ Ground state solutions for a semilinear elliptic problem with critical-subcritical growth

Cites Work

• Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains
• On some variational problems
• A nonlinear elliptic equation with critical exponents: Effect of geometry and topology of the domain
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence and multiplicity of solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Fractional integration operator of variable order in the Hölder spaces \(H^{\lambda (x)}\)
• Existence of infinitely many solutions for a Neumann problem involving the \(p(x)\)-Laplacian
• Entire solutions of multivalued nonlinear Schrödinger equations in Sobolev spaces with variable exponent
• Solutions for \(p(x)\)-Laplacian Dirichlet problems with singular coefficients
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
• Remarks on some quasilinear elliptic equations
• A class of De Giorgi type and Hölder continuity
• Sobolev embeddings with variable exponent
• Fractional integrals and singular integrals in the holder classes of variable order
• Integral Functionals and the Gap Problem: Sharp Bounds for Relaxation and Energy Concentration
• Existence of Solutions for a Class of Problems in IR N Involving the p(x)-Laplacian
• Regularity results for a class of functionals with non-standard growth
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
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