Conformal spectral stability estimates for the Neumann Laplacian

被引：6

作者：

Burenkov, V. I. ^{[1
,2
]}

Gol'dshtein, V. ^{[3
]}

Ukhlov, A. ^{[3
]}

机构：

[1] Peoples Friendship Univ Russia, 6 Mikluho Maklay St, Moscow, Russia

[2] Steklov Math Inst, 8 Gubkin St, Moscow, Russia

[3] Ben Gurion Univ Negev, POB 653, IL-84105 Beer Sheva, Israel

来源：

MATHEMATISCHE NACHRICHTEN | 2016年 / 289卷 / 17-18期

关键词：

eigenvalue problem; elliptic equations; conformal mappings; quasidiscs; EIGENVALUES; OPERATORS; DIMENSION;

D O I：

10.1002/mana.201500439

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the eigenvalue problem for the Neumann-Laplace operator in conformal regular planar domains Omega subset of C. Conformal regular domains support the Poincare-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. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：2133 / 2146

页数：14

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