Spectral stability estimates of neumann divergence form elliptic operators

VLADIMIR GOL'DSHTEIN; VALERII PCHELINTSEV; ALEXANDER UKHLOV

Spectral stability estimates of neumann divergence form elliptic operators

VLADIMIR GOL'DSHTEIN, VALERII PCHELINTSEV, ALEXANDER UKHLOV

Department of Mathematics

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

2 Scopus citations

Abstract

We study spectral stability estimates of elliptic operators in divergence form -div[A(w)rg(w)] with the Neumann boundary condition in domains Ω C which satisfy the quasihyperbolic boundary condition. This class of domains includes Lipschitz domains, Hölder singular domains and some fractal type domains like snowakes. The suggested method is based on connections of quasiconformal mappings and Sobolev spaces with applications to the Poincare type inequalities.

Original language	English
Pages (from-to)	131-147
Number of pages	17
Journal	Mathematical Reports
Volume	23
Issue number	1-2
State	Published - 1 Jan 2021

Keywords

Elliptic equations
Quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

Cite this

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title = "Spectral stability estimates of neumann divergence form elliptic operators",

abstract = "We study spectral stability estimates of elliptic operators in divergence form -div[A(w)rg(w)] with the Neumann boundary condition in domains Ω C which satisfy the quasihyperbolic boundary condition. This class of domains includes Lipschitz domains, H{\"o}lder singular domains and some fractal type domains like snowakes. The suggested method is based on connections of quasiconformal mappings and Sobolev spaces with applications to the Poincare type inequalities.",

keywords = "Elliptic equations, Quasiconformal mappings, Sobolev spaces",

author = "VLADIMIR GOL'DSHTEIN and VALERII PCHELINTSEV and ALEXANDER UKHLOV",

note = "Funding Information: Acknowledgments. The first author was supported by the United States-Israel Bina- Funding Information: tional 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) and RFBR Grant No. 18-31-00011. Publisher Copyright: {\textcopyright} 2021 Editura Academiei Romane. All rights reserved.",

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AU - GOL'DSHTEIN, VLADIMIR

AU - PCHELINTSEV, VALERII

AU - UKHLOV, ALEXANDER

N1 - Funding Information: Acknowledgments. The first author was supported by the United States-Israel Bina- Funding Information: tional 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) and RFBR Grant No. 18-31-00011. Publisher Copyright: © 2021 Editura Academiei Romane. All rights reserved.

PY - 2021/1/1

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N2 - We study spectral stability estimates of elliptic operators in divergence form -div[A(w)rg(w)] with the Neumann boundary condition in domains Ω C which satisfy the quasihyperbolic boundary condition. This class of domains includes Lipschitz domains, Hölder singular domains and some fractal type domains like snowakes. The suggested method is based on connections of quasiconformal mappings and Sobolev spaces with applications to the Poincare type inequalities.

AB - We study spectral stability estimates of elliptic operators in divergence form -div[A(w)rg(w)] with the Neumann boundary condition in domains Ω C which satisfy the quasihyperbolic boundary condition. This class of domains includes Lipschitz domains, Hölder singular domains and some fractal type domains like snowakes. The suggested method is based on connections of quasiconformal mappings and Sobolev spaces with applications to the Poincare type inequalities.

KW - Elliptic equations

KW - Quasiconformal mappings

KW - Sobolev spaces

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JO - Mathematical Reports

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IS - 1-2

ER -

Spectral stability estimates of neumann divergence form elliptic operators

Abstract

Keywords

ASJC Scopus subject areas

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