Conformal Weights and Sobolev Embeddings

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Abstract

We study embeddings of the Sobolev space W12(Ω) into weighted Lebesgue spaces L q(Ω, h) with the so-called universal conformal weight h defined as the Jacobian of a conformal homeomorphism φ from Ω onto the unit disk in the complex plane. Applications to elliptic boundary value problems are discussed. Bibliography: 17 titles.

Original languageEnglish
Pages (from-to)202-210
Number of pages9
JournalJournal of Mathematical Sciences
Volume193
Issue number2
DOIs
StatePublished - 1 Aug 2013

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