Weak quasiconformal mappings and weighted poincarÉ-sobolev inequalities

Alexander Menovschikov; Alexander Ukhlov

Weak quasiconformal mappings and weighted poincarÉ-sobolev inequalities

Alexander Menovschikov, Alexander Ukhlov

Department of Mathematics

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

Abstract

In the article, we prove weighted Sobolev inequalities with weights which are Jacobians of mappings inverse to weak quasiconformal mappings. On this base, we obtain estimates of the first non-trivial eigenvalue of the two-dimensional Neumann-Laplacian in Hölder singular domains.

Original language	English
Pages (from-to)	541-553
Number of pages	13
Journal	Pure and Applied Functional Analysis
Volume	9
Issue number	2
State	Published - 1 Jan 2024

Keywords

Quasiconformal mappings
Sobolev inequalities
Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics
Control and Optimization

Cite this

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title = "Weak quasiconformal mappings and weighted poincar{\'E}-sobolev inequalities",

abstract = "In the article, we prove weighted Sobolev inequalities with weights which are Jacobians of mappings inverse to weak quasiconformal mappings. On this base, we obtain estimates of the first non-trivial eigenvalue of the two-dimensional Neumann-Laplacian in H{\"o}lder singular domains.",

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AB - In the article, we prove weighted Sobolev inequalities with weights which are Jacobians of mappings inverse to weak quasiconformal mappings. On this base, we obtain estimates of the first non-trivial eigenvalue of the two-dimensional Neumann-Laplacian in Hölder singular domains.

KW - Quasiconformal mappings

KW - Sobolev inequalities

KW - Sobolev spaces

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Weak quasiconformal mappings and weighted poincarÉ-sobolev inequalities

Abstract

Keywords

ASJC Scopus subject areas

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