On conformal spectral gap estimates of the Dirichlet–Laplacian
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- by V. Gol′dshtein, V. Pchelintsev and A. Ukhlov
- St. Petersburg Math. J. 31 (2020), 325-335
- DOI: https://doi.org/10.1090/spmj/1599
- Published electronically: February 4, 2020
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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.References
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Bibliographic Information
- V. Gol′dshtein
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O.Box 653, 8410501, Beer Sheva, Israel
- MR Author ID: 197069
- Email: vladimir@math.bgu.ac.il
- V. Pchelintsev
- Affiliation: Division of Mathematics and Informatics, Tomsk Polytechnic University, Lenin pr. 30, 634050, Tomsk, Russia; and International Laboratory SSP & QF, Tomsk State University, Lenin pr. 36, 634050, Tomsk, Russia
- Address at time of publication: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 8410501, Beer Sheva, Israel
- MR Author ID: 1018625
- Email: vpchelintsev@vtomske.ru
- A. Ukhlov
- Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 8410501, Beer Sheva, Israel
- MR Author ID: 336276
- Email: ukhlov@math.bgu.ac.il
- Received by editor(s): October 10, 2018
- Published electronically: February 4, 2020
- Additional Notes: The first author was supported by the United States–Israel Binational Science Foundation (BSF Grant no. 2014055).
The second author was partially supported by the Ministry of Education and Science of the Russian Federation in the framework of the research Project no. 2.3208.2017/4.6, by RFBR Grant no. 18-31-00011. - © Copyright 2020 American Mathematical Society
- Journal: St. Petersburg Math. J. 31 (2020), 325-335
- MSC (2010): Primary 35P15; Secondary 46E35, 30C65
- DOI: https://doi.org/10.1090/spmj/1599
- MathSciNet review: 3937503
Dedicated: Dedicated to V. Maz’ya on the occasion of his 80th birthday