Space quasiconformal mappings and Neumann eigenvalues in fractal type domains

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

Research output: Contribution to journalArticleScientificpeer-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 languageEnglish
JournalGeorgian Mathematical Journal
Volume25
Issue number2
Pages (from-to)221-233
Number of pages13
ISSN1072-947X
DOIs
Publication statusPublished - 1 Jun 2018
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 111 Mathematics

Cite this

Gol'dshtein, Vladimir ; Hurri-Syrjänen, Ritva ; Ukhlov, Alexander. / Space quasiconformal mappings and Neumann eigenvalues in fractal type domains. In: Georgian Mathematical Journal. 2018 ; Vol. 25, No. 2. pp. 221-233.
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Space quasiconformal mappings and Neumann eigenvalues in fractal type domains. / Gol'dshtein, Vladimir; Hurri-Syrjänen, Ritva; Ukhlov, Alexander.

In: Georgian Mathematical Journal, Vol. 25, No. 2, 01.06.2018, p. 221-233.

Research output: Contribution to journalArticleScientificpeer-review

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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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