Conformal Weights and Sobolev Embeddings

V. Gol'dshtein; A. Ukhlov

doi:10.1007/s10958-013-1447-x

Conformal Weights and Sobolev Embeddings

V. Gol'dshtein, A. Ukhlov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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 language	English
Pages (from-to)	202-210
Number of pages	9
Journal	Journal of Mathematical Sciences
Volume	193
Issue number	2
DOIs	https://doi.org/10.1007/s10958-013-1447-x
State	Published - 1 Aug 2013

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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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.",

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AB - 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.

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Conformal Weights and Sobolev Embeddings

Abstract

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