Neumann eigenvalues of elliptic operators in Sobolev extension domains

Vladimir Gol’dshtein; Valerii Pchelintsev; Alexander Ukhlov

doi:10.1007/s13324-024-00926-x

Neumann eigenvalues of elliptic operators in Sobolev extension domains

Vladimir Gol’dshtein, Valerii Pchelintsev, Alexander Ukhlov

Department of Mathematics

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

Abstract

We obtain estimates of Neumann eigenvalues of the divergence form elliptic operators in Sobolev extension domains. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. The connection between Neumann eigenvalues of elliptic operators and the smallest-circle problem (initially suggested by J. J. Sylvester in 1857) is given.

Original language	English
Article number	64
Journal	Analysis and Mathematical Physics
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s13324-024-00926-x
State	Published - 1 Jun 2024

Keywords

30C65
35P15
46E35
Elliptic equations
Extension operators
Sobolev spaces

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Mathematical Physics

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10.1007/s13324-024-00926-x

Cite this

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abstract = "We obtain estimates of Neumann eigenvalues of the divergence form elliptic operators in Sobolev extension domains. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. The connection between Neumann eigenvalues of elliptic operators and the smallest-circle problem (initially suggested by J. J. Sylvester in 1857) is given.",

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Y1 - 2024/6/1

N2 - We obtain estimates of Neumann eigenvalues of the divergence form elliptic operators in Sobolev extension domains. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. The connection between Neumann eigenvalues of elliptic operators and the smallest-circle problem (initially suggested by J. J. Sylvester in 1857) is given.

AB - We obtain estimates of Neumann eigenvalues of the divergence form elliptic operators in Sobolev extension domains. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. The connection between Neumann eigenvalues of elliptic operators and the smallest-circle problem (initially suggested by J. J. Sylvester in 1857) is given.

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KW - 35P15

KW - 46E35

KW - Elliptic equations

KW - Extension operators

KW - Sobolev spaces

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Neumann eigenvalues of elliptic operators in Sobolev extension domains

Abstract

Keywords

ASJC Scopus subject areas

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