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

Date:	2015
Abstract:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Compactness ; Sobolev space ; Rearrangement-invariant space ; Isoperi- metric function ; Almost-compact embedding ; John domain ; Maz'ya domain ; Product probability space ; Integral operator
Published in:	Publicacions matemàtiques, Vol. 59 Núm. 2 (2015) , p. 373-448 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/295191
DOI: 10.5565/PUBLMAT_59215_06

31 p, 614.3 KB

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