Vector-valued Lizorkin-Triebel spaces and sharp trace theory for functions in Sobolev spaces with mixed $ \pmb{L_p}$-norm for parabolic problems

DOI10.1070/SM2005v196n06ABEH000900zbMath1092.46025OpenAlexW1996220554MaRDI QIDQ5713316

Peter Weidemaier

Publication date: 14 December 2005

Published in: Sbornik: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm2005v196n06abeh000900

zbMATH Keywords

Sobolev spacesparabolic partial differential equationsLizorkin-Triebel spacesDirichlet problem, Neumann problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Spaces of vector- and operator-valued functions (46E40)

Related Items (11)

Maximal \(L^1\)-regularity for parabolic initial-boundary value problems with inhomogeneous data ⋮ Traces of vector-valued Sobolev spaces ⋮ Some problems for Petrovskii parabolic systems in generalized Sobolev spaces ⋮ Anisotropic Lizorkin-Triebel spaces with mixed norms - traces on smooth boundaries ⋮ Characterisation by local means of anisotropic Lizorkin-Triebel spaces with mixed norms ⋮ Maximal \(L^1\)-regularity for parabolic boundary value problems with inhomogeneous data in the half-space ⋮ Anisotropic, mixed-norm Lizorkin-Triebel spaces and diffeomorphic maps ⋮ Traces and embeddings of anisotropic function spaces ⋮ On solvability of an initial-boundary-value problem for equations of magnetohydrodynamics ⋮ Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm ⋮ Maximal \(L^1\)-regularity of the heat equation and application to a free boundary problem of the Navier-Stokes equations near the half-space

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