A compact embedding of a Sobolev space is equivalent to an embedding into a better space

DOI10.1090/S0002-9939-10-10390-6zbMath1203.46020OpenAlexW2065240585MaRDI QIDQ4929994

Zhuomin Liu, Piotr Hajłasz

Publication date: 27 September 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-10-10390-6

zbMATH Keywords

Orlicz-Sobolev spacecompact embedding

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)

Related Items (8)

Quasilinear elliptic equations on noncompact Riemannian manifolds ⋮ Sobolev embeddings in infinite dimensions ⋮ Existence and regularity results for nonlinear elliptic equations in Orlicz spaces ⋮ Elliptic problems with convection terms in Orlicz spaces ⋮ Deterministic homogenization of nonlinear degenerate elliptic operators with nonstandard growth ⋮ Weak solution for Neumann \((p,q)\)-Laplacian problem on Riemannian manifold ⋮ An elliptic equation on n-dimensional manifolds ⋮ Poincaré inequalities and compact embeddings from Sobolev type spaces into weighted \(L^q\) spaces on metric spaces

Cites Work

• A sharp embedding theorem for Orlicz-Sobolev spaces
• Compactness of Sobolev imbeddings involving rearrangement-invariant norms
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