Space quasiconformal composition operators with applications to Neumann eigenvalues

Vladimir Gol’dshtein; Ritva Hurri-Syrjänen; Valerii Pchelintsev; Alexander Ukhlov

doi:https://doi.org/10.1007/s13324-020-00420-0

Space quasiconformal composition operators with applications to Neumann eigenvalues

Vladimir Gol’dshtein, Ritva Hurri-Syrjänen, Valerii Pchelintsev, Alexander Ukhlov

Department of Mathematics

Ben-Gurion University of the Negev

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

Abstract

In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

Original language	American English
Article number	78
Journal	Analysis and Mathematical Physics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s13324-020-00420-0
State	Published - 1 Dec 2020

Keywords

Elliptic equations
Quasiconformal mappings
Sobolev spaces

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Mathematical Physics

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https://doi.org/10.1007/s13324-020-00420-0

Cite this

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AU - Gol’dshtein, Vladimir

AU - Hurri-Syrjänen, Ritva

AU - Pchelintsev, Valerii

AU - Ukhlov, Alexander

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

AB - In this article we obtain estimates of Neumann eigenvalues of p-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev–Poincaré-inequalities. By using a sharp version of the reverse Hölder inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

KW - Elliptic equations

KW - Quasiconformal mappings

KW - Sobolev spaces

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JO - Analysis and Mathematical Physics

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ER -

Space quasiconformal composition operators with applications to Neumann eigenvalues

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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