4.2 Article

Almost compact and compact embeddings of variable exponent spaces

Journal

STUDIA MATHEMATICA
Volume 268, Issue 2, Pages 187-212

Publisher

POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
DOI: 10.4064/sm211206-24-2

Keywords

almost compact embeddings; Banach function spaces; variable Lebesgue spaces; variable Sobolev spaces

Categories

Ask authors/readers for more resources

This article provides necessary and sufficient conditions for embedding variable exponent spaces and presents conditions for compact embedding of Sobolev spaces based on variable exponent spaces. The article also includes previous results as special cases.
Let Omega be an open subset of R-N, and let p, q : Omega -> [1, infinity] be measurable functions. We give a necessary and sufficient condition for the embedding of the variable exponent space L-p(center dot)(Omega) in L-q(center dot)(Omega) to be almost compact. This leads to a condition on Omega, p and q sufficient to ensure that the Sobolev space W-1,W-p(center dot)(Omega) based on L-p(center dot)(Omega) is compactly embedded in L-q(center dot)(Omega); compact embedding results of this type already in the literature are included as special cases.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.2
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available