Abstract
We study spectral stability estimates of the Dirichlet eigenvalues of the Laplacian in nonconvex domains Ω ⊂ ℝ2. 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.
Original language | English |
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Pages (from-to) | 325-335 |
Number of pages | 11 |
Journal | St. Petersburg Mathematical Journal |
Volume | 31 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jan 2020 |
Keywords
- Conformal mappings
- Elliptic equations
- Sobolev spaces
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics