Spectral stability estimates of Dirichlet divergence form elliptic operators

Vladimir Gol’dshtein; Valerii Pchelintsev; Alexander Ukhlov

doi:10.1007/s13324-020-00425-9

Spectral stability estimates of Dirichlet divergence form elliptic operators

Department of Mathematics

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Abstract

We study spectral stability estimates of elliptic operators in divergence form - div [A(w) ∇ g(w)] with the Dirichlet boundary condition in non-Lipschitz domains Ω~ ⊂ C. The suggested method is based on the theory of quasiconformal mappings, weighted Sobolev spaces theory and its applications to the Poincaré inequalities.

Original language	English
Article number	74
Journal	Analysis and Mathematical Physics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1007/s13324-020-00425-9
State	Published - 1 Dec 2020

Keywords

Elliptic equations
Quasiconformal mappings
Sobolev spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-020-00425-9

Cite this

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

abstract = "We study spectral stability estimates of elliptic operators in divergence form - div [A(w) ∇ g(w)] with the Dirichlet boundary condition in non-Lipschitz domains Ω\textasciitilde{} ⊂ C. The suggested method is based on the theory of quasiconformal mappings, weighted Sobolev spaces theory and its applications to the Poincar{\'e} inequalities.",

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

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AU - Gol’dshtein, Vladimir

AU - Pchelintsev, Valerii

AU - Ukhlov, Alexander

PY - 2020/12/1

Y1 - 2020/12/1

N2 - We study spectral stability estimates of elliptic operators in divergence form - div [A(w) ∇ g(w)] with the Dirichlet boundary condition in non-Lipschitz domains Ω~ ⊂ C. The suggested method is based on the theory of quasiconformal mappings, weighted Sobolev spaces theory and its applications to the Poincaré inequalities.

AB - We study spectral stability estimates of elliptic operators in divergence form - div [A(w) ∇ g(w)] with the Dirichlet boundary condition in non-Lipschitz domains Ω~ ⊂ C. The suggested method is based on the theory of quasiconformal mappings, weighted Sobolev spaces theory and its applications to the Poincaré inequalities.

KW - Elliptic equations

KW - Quasiconformal mappings

KW - Sobolev spaces

UR - https://www.scopus.com/pages/publications/85095709066

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DO - 10.1007/s13324-020-00425-9

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AN - SCOPUS:85095709066

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VL - 10

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

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ER -

Spectral stability estimates of Dirichlet divergence form elliptic operators

Abstract

Keywords

ASJC Scopus subject areas

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