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Kompaktnost Sobolevových vnoření vyššího řádu / Compactness of higher-order Sobolev embeddings

The present work deals with m-th order compact Sobolev embeddings on a do- main Ω ⊆ Rn endowed with a probability measure ν and satisfying certain isoperi- metric inequality. We derive a condition on a pair of rearrangement-invariant spaces X(Ω, ν) and Y (Ω, ν) which suffices to guarantee a compact embedding of the Sobolev space V m X(Ω, ν) into Y (Ω, ν). The condition is given in terms of compactness of certain operator on representation spaces. This result is then applied to characterize higher-order compact Sobolev embeddings on concrete measure spaces, including John domains, Maz'ya classes of Euclidean domains and product probability spaces, among them the Gauss space is the most stan- dard example. 1

Identiferoai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:304107
Date January 2012
CreatorsSlavíková, Lenka
ContributorsPick, Luboš, Nekvinda, Aleš
Source SetsCzech ETDs
LanguageEnglish
Detected LanguageEnglish
Typeinfo:eu-repo/semantics/masterThesis
Rightsinfo:eu-repo/semantics/restrictedAccess

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