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Algebra i Analiz, 2019, Volume 31, Issue 2, Pages 189–203 (Mi aa1643)  
This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

On conformal spectral gap estimates of the Dirichlet-Laplacian

V. Gol'dshteina, V. Pchelintsevbac, A. Ukhlova

a Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 8410501, Beer Sheva, Israel
b International Laboratory SSP & QF, Tomsk State University, Lenin pr., 36, 634050, Tomsk, Russia
c Division of Mathematics and Informatics, Tomsk Polytechnic University, Lenin pr., 30, 634050, Tomsk, Russia
Full-text PDF (246 kB) Citations (3)
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Abstract: We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains $ \Omega \subset \mathbb{R}^2$. With the help of these estimates, we obtain asymptotically sharp inequalities of ratios of eigenvalues in the framework of the Payne-Pólya-Weinberger inequalities. These estimates are equivalent to spectral gap estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains in terms of conformal (hyperbolic) geometry.
Keywords: elliptic equations, Sobolev spaces, conformal mappings.
Funding agency Grant number
United States - Israel Binational Science Foundation (BSF) 2014055
Ministry of Education and Science of the Russian Federation 2.3208.2017/4.6
Russian Foundation for Basic Research 18-31-00011
The first author was supported by the United States–Israel Binational Science Foundation (BSF Grant no. 2014055).
Received: 10.10.2018
English version:
St. Petersburg Mathematical Journal, 2019, Volume 31, Issue 2, Pages 325–335
DOI: https://doi.org/10.1090/spmj/1599
Bibliographic databases:
Document Type: Article
MSC: Primary 35P15; Secondary 46E35, 30C65
Language: English
Citation: V. Gol'dshtein, V. Pchelintsev, A. Ukhlov, “On conformal spectral gap estimates of the Dirichlet-Laplacian”, Algebra i Analiz, 31:2 (2019), 189–203; St. Petersburg Math. J., 31:2 (2019), 325–335
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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