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Compactness of higher-order Sobolev embeddings
Slavíková, Lenka (Univerzita Karlova (Praga, República Txeca). Department of Mathematical Analysis)

Data: 2015
Resum: We study higher-order compact Sobolev embeddings on a domain ∩ ⊆Rn endowed with a probability measure ∨ and satisfying certain isoperimetric inequality. Given m ∈ N, we present a condition on a pair of rearrangement-invariant spaces X( ∩,∨) and Y ( ∩,∨) which suffices to guarantee a compact embedding of the Sobolev space V m X ( ∩,∨) into Y (∩,∨). The condition is given in terms of compactness of certain one-dimensional operator depending on the isoperimetric function of ( ∩,∨). We then apply this result to the characterization of higher-order compact Sobolev embeddings on concrete measure spaces, including John domains, Maz'ya classes of Euclidean domains and product probability spaces, whose standard example is the Gauss space.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Compactness ; Sobolev space ; Rearrangement-invariant space ; Isoperi- metric function ; Almost-compact embedding ; John domain ; Maz'ya domain ; Product probability space ; Integral operator
Publicat a: Publicacions matemàtiques, Vol. 59 Núm. 2 (2015) , p. 373–448 (Articles) , ISSN 2014-4350

Adreça original:
DOI: 10.5565/PUBLMAT_59215_06

31 p, 614.3 KB

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