Conformal spectral stability estimates for the Neumann Laplacian

V. I. Burenkov; V. Gol'dshtein; A. Ukhlov

doi:10.1002/mana.201500439

Conformal spectral stability estimates for the Neumann Laplacian

V. I. Burenkov, V. Gol'dshtein, A. Ukhlov

Department of Mathematics

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

8 Scopus citations

Abstract

We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω ⊂ C. Conformal regular domains support the Poincaré–Sobolev inequality and this allows us to estimate the variation of the eigenvalues of the Neumann Laplacian upon domain perturbation via energy type integrals. Boundaries of such domains can have any Hausdorff dimension between one and two.

Original language	English
Pages (from-to)	2133-2146
Number of pages	14
Journal	Mathematische Nachrichten
Volume	289
Issue number	17-18
DOIs	https://doi.org/10.1002/mana.201500439
State	Published - 1 Dec 2016

Keywords

conformal mappings
eigenvalue problem
elliptic equations
quasidiscs

ASJC Scopus subject areas

General Mathematics

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10.1002/mana.201500439

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abstract = "We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω ⊂ C. Conformal regular domains support the Poincar{\'e}–Sobolev inequality and this allows us to estimate the variation of the eigenvalues of the Neumann Laplacian upon domain perturbation via energy type integrals. Boundaries of such domains can have any Hausdorff dimension between one and two.",

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AU - Gol'dshtein, V.

AU - Ukhlov, A.

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N2 - We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω ⊂ C. Conformal regular domains support the Poincaré–Sobolev inequality and this allows us to estimate the variation of the eigenvalues of the Neumann Laplacian upon domain perturbation via energy type integrals. Boundaries of such domains can have any Hausdorff dimension between one and two.

AB - We study the eigenvalue problem for the Neumann–Laplace operator in conformal regular planar domains Ω ⊂ C. Conformal regular domains support the Poincaré–Sobolev inequality and this allows us to estimate the variation of the eigenvalues of the Neumann Laplacian upon domain perturbation via energy type integrals. Boundaries of such domains can have any Hausdorff dimension between one and two.

KW - conformal mappings

KW - eigenvalue problem

KW - elliptic equations

KW - quasidiscs

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JF - Mathematische Nachrichten

IS - 17-18

ER -

Conformal spectral stability estimates for the Neumann Laplacian

Abstract

Keywords

ASJC Scopus subject areas

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