Some counterexamples for the theory of sobolev spaces on bad domains.

Autor: Maz'ya, Vladimir, Netrusov, Yuri
Zdroj: Potential Analysis; Feb1995, Vol. 4 Issue 1, p47-65, 19p
Abstrakt: It is shown that some well-known properties of the Sobolev space L(Ω) do not admit extension to the space L(Ω) of the functions with l-th order derivatives in L(Ω), l>1, without requirements to the domain Ω. Namely, we give examples of Ω such that In the Appendix necessary and sufficient conditions are given for the imbeddings L(Ω)⊂ L(Ω, μ) and H( R)⊂ L( R, μ), where p≥1, p> q>0, μ is a measure and H(Ω) is the Bessel potential space, 1< p<∞, l>0. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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