Compact embedding for \(p(x,t)\)-Sobolev spaces and existence theory to parabolic equations with \(p(x,t)\)-growth

DOI10.1007/s13163-016-0211-4zbMath1365.35086OpenAlexW2522693397MaRDI QIDQ506414

André H. Erhardt

Publication date: 31 January 2017

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13163-016-0211-4

zbMATH Keywords

nonstandard growthcompactness theoremexistence theorynonlinear parabolic problemsnonstandard parabolic Lebesgue and Sobolev spaces

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Embedding (54C25) Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators (35K86)

Related Items

The stability of parabolic problems with nonstandard \(p(x,t)\)-growth ⋮ Stability for evolution equations with variable growth ⋮ On the continuity of solutions of the nonhomogeneous evolution \(p(x, t)\)-Laplace equation ⋮ On solutions of a parabolic equation with nonstandard growth condition ⋮ Existence and regularity results for a class of parabolic problems with double phase flux of variable growth ⋮ Regularity and existence of solutions to parabolic equations with nonstandard p(x,t),q(x,t)-growth conditions ⋮ Strong solutions of evolution equations with \(p(x,t)\)-Laplacian: existence, global higher integrability of the gradients and second-order regularity ⋮ Existence of weak solutions to a certain homogeneous parabolic Neumann problem involving variable exponents and cross-diffusion ⋮ Time periodic solutions for strongly nonlinear parabolic systems with \(p(x)\)-growth conditions

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