Compact trace in weighted variable exponent Sobolev spaces \(W^{1,p(x)}(\Omega;v_0,v_1)\)

DOI10.1016/j.jmaa.2008.08.004zbMath1159.46020OpenAlexW1646592452MaRDI QIDQ950471

Qiao Liu

Publication date: 22 October 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.2008.08.004

zbMATH Keywords

compact embeddingextension operatorcompact traceweighted variable exponent Lebesgue spaceweighted variable exponent Sobolev space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

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Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted \(p(.)\)-Laplacian ⋮ On some degenerate quasilinear equations involving variable exponents ⋮ Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted p (·)-Laplacian ⋮ Unnamed Item ⋮ The Kolmogorov-Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces ⋮ The maximal operator on weighted variable Lebesgue spaces

Cites Work

• Existence of radial solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Some embeddings of weighted Sobolev spaces on finite measure and quasibounded domains
• Existence of solutions in weighted Sobolev spaces for some degenerate semilinear elliptic equations.
• Semilinear elliptic problems with nonlinear boundary conditions in unbounded domains
• Minimax theorems
• Boundary trace embedding theorems for variable exponent Sobolev spaces
• Compact imbeddings of weighted Sobolev spaces on unbounded domains
• Solutions for \(p(x)\)-Laplacian Dirichlet problems with singular coefficients
• Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spacesLp(·) andWk,p(·)
• OnL^p(x)norms
• Imbedding Theorems for Weighted Orlicz-Sobolev Spaces
• Nonlinear boundary value problems in weighted sobolev spaces
• Sobolev embeddings with variable exponent
• Variable exponent trace spaces
• Compact imbedding theorems with symmetry of Strauss-Lions type for the space \(W^{1,p(x)}(\Omega)\)
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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