Compactness of higher-order Sobolev embeddings
Slavíková, Lenka (Univerzita Karlova (Praga, República Txeca). Department of Mathematical Analysis)
Fecha: |
2015 |
Resumen: |
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. |
Derechos: |
Tots els drets reservats. |
Lengua: |
Anglès |
Documento: |
Article ; recerca ; Versió publicada |
Materia: |
Compactness ;
Sobolev space ;
Rearrangement-invariant space ;
Isoperi- metric function ;
Almost-compact embedding ;
John domain ;
Maz'ya domain ;
Product probability space ;
Integral operator |
Publicado en: |
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
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