Space quasiconformal mappings and Neumann eigenvalues in fractal type domains

Vladimir Gol'Dshtein; Ritva Hurri-Syrjänen; Alexander Ukhlov

doi:10.1515/gmj-2018-0025

Space quasiconformal mappings and Neumann eigenvalues in fractal type domains

Vladimir Gol'Dshtein, Ritva Hurri-Syrjänen, Alexander Ukhlov

Department of Mathematics

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

4 Scopus citations

Abstract

We study the variation of Neumann eigenvalues of the p-Laplace operator under quasiconformal perturbations of space domains. This study allows us to obtain the lower estimates of Neumann eigenvalues in fractal type domains. The proposed approach is based on the geometric theory of composition operators in connection with the quasiconformal mapping theory.

Original language	English
Pages (from-to)	221-233
Number of pages	13
Journal	Georgian Mathematical Journal
Volume	25
Issue number	2
DOIs	https://doi.org/10.1515/gmj-2018-0025
State	Published - 1 Jun 2018

Keywords

Neumann eigenvalues
Sobolev spaces
quasiconformal mappings

ASJC Scopus subject areas

General Mathematics

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10.1515/gmj-2018-0025

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title = "Space quasiconformal mappings and Neumann eigenvalues in fractal type domains",

abstract = "We study the variation of Neumann eigenvalues of the p-Laplace operator under quasiconformal perturbations of space domains. This study allows us to obtain the lower estimates of Neumann eigenvalues in fractal type domains. The proposed approach is based on the geometric theory of composition operators in connection with the quasiconformal mapping theory.",

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AU - Ukhlov, Alexander

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AB - We study the variation of Neumann eigenvalues of the p-Laplace operator under quasiconformal perturbations of space domains. This study allows us to obtain the lower estimates of Neumann eigenvalues in fractal type domains. The proposed approach is based on the geometric theory of composition operators in connection with the quasiconformal mapping theory.

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KW - quasiconformal mappings

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Space quasiconformal mappings and Neumann eigenvalues in fractal type domains

Abstract

Keywords

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