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 Math. Nachr., 2016, Volume 289, Issue 17, Pages 2133–2146 (Mi matna4)

Conformal spectral stability estimates for the Neumann Laplacian

V. I. Burenkovab, V. Gol'dshteinc, A. Ukhlovc

a Peoples' Friendship University of Russia, Moscow, 6 Mikluho-Maklay St., Russia
b Steklov Mathematical Institute, Moscow, 8 Gubkin St., Russia
c Ben-Gurion University of the Negev, P.O. Box 653, 84105, Beer-Sheva, Israel

Abstract: We study the eigenvalue problem for the Neumann-–Laplace operator in conformal regular planar domains $\Omega\subset\mathbb C$. 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.

 Funding Agency Grant Number United States - Israel Binational Science Foundation (BSF) 2014055 Funded by United States-Israel Binational Science Foundation. Grant Number: 2014055

DOI: https://doi.org/10.1002/mana.201500439

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Accepted:18.02.2017
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