Quasiconformal mappings and Neumann eigenvalues of divergent elliptic operators

V. Gol'dshtein; V. Pchelintsev; A. Ukhlov

doi:10.1080/17476933.2021.1921752

Quasiconformal mappings and Neumann eigenvalues of divergent elliptic operators

V. Gol'dshtein, V. Pchelintsev, A. Ukhlov

Department of Mathematics

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

2 Scopus citations

Abstract

We study spectral properties of divergence form elliptic operators (Formula presented.) with the Neumann boundary condition in planar domains (including some fractal type domains) that satisfy to the quasihyperbolic boundary conditions. Our method is based on an interplay between quasiconformal mappings, elliptic operators and composition operators on Sobolev spaces.

Original language	English
Pages (from-to)	2281-2302
Number of pages	22
Journal	Complex Variables and Elliptic Equations
Volume	67
Issue number	9
DOIs	https://doi.org/10.1080/17476933.2021.1921752
State	Published - 1 Jan 2022

Keywords

30C62
35J15
46E35
Elliptic equations
Sobolev spaces
quasiconformal mappings

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1080/17476933.2021.1921752

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abstract = "We study spectral properties of divergence form elliptic operators (Formula presented.) with the Neumann boundary condition in planar domains (including some fractal type domains) that satisfy to the quasihyperbolic boundary conditions. Our method is based on an interplay between quasiconformal mappings, elliptic operators and composition operators on Sobolev spaces.",

keywords = "30C62, 35J15, 46E35, Elliptic equations, Sobolev spaces, quasiconformal mappings",

author = "V. Gol'dshtein and V. Pchelintsev and A. Ukhlov",

note = "Funding Information: The first author was supported by the United States-Israel Binational Science Foundation (BSF Grant No. 2014055). The second author was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2020-1479/1). Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",

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AU - Gol'dshtein, V.

AU - Pchelintsev, V.

AU - Ukhlov, A.

N1 - Funding Information: The first author was supported by the United States-Israel Binational Science Foundation (BSF Grant No. 2014055). The second author was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2020-1479/1). Publisher Copyright: © 2021 Informa UK Limited, trading as Taylor & Francis Group.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - We study spectral properties of divergence form elliptic operators (Formula presented.) with the Neumann boundary condition in planar domains (including some fractal type domains) that satisfy to the quasihyperbolic boundary conditions. Our method is based on an interplay between quasiconformal mappings, elliptic operators and composition operators on Sobolev spaces.

AB - We study spectral properties of divergence form elliptic operators (Formula presented.) with the Neumann boundary condition in planar domains (including some fractal type domains) that satisfy to the quasihyperbolic boundary conditions. Our method is based on an interplay between quasiconformal mappings, elliptic operators and composition operators on Sobolev spaces.

KW - 30C62

KW - 35J15

KW - 46E35

KW - Elliptic equations

KW - Sobolev spaces

KW - quasiconformal mappings

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JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 9

ER -

Quasiconformal mappings and Neumann eigenvalues of divergent elliptic operators

Abstract

Keywords

ASJC Scopus subject areas

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