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

Ben-Gurion University of the Negev

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

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	American 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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1002/mana.201500439

Cite this

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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 - Burenkov, V. I.

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

UR - http://www.scopus.com/inward/record.url?scp=84963818989&partnerID=8YFLogxK

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DO - 10.1002/mana.201500439

M3 - Article

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SP - 2133

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JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 17-18

ER -

Conformal spectral stability estimates for the Neumann Laplacian

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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