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

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

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
Journal	Georgian Mathematical Journal
Volume	25
Issue number	2
Pages (from-to)	221-233
Number of pages	13
ISSN	1072-947X
DOIs	https://doi.org/10.1515/gmj-2018-0025
Publication status	Published - 1 Jun 2018
MoE publication type	A1 Journal article-refereed

Fields of Science

111 Mathematics

Access to Document

10.1515/gmj-2018-0025

GHSU2018Accepted author manuscript, 471 KBLicence: Unspecified

Cite this

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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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DO - 10.1515/gmj-2018-0025

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