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- Title
Spectral Estimates of the Dirichlet-Laplace Operator in Conformal Regular Domains.
- Authors
Kolesnikov, Ivan; Pchelintsev, Valerii
- Abstract
We consider conformal spectral estimates of the Dirichlet–Laplace operator in conformal regular domains Ω ⊂ ℝ2, based on the geometric theory of composition operators on Sobolev spaces, which permits us to estimate constants in the Poincaré-Sobolev inequalities. We obtain lower estimates for the first eigenvalue of the Dirichlet–Laplace operator in the class of conformal regular domains and conformal estimates for the ground state energy of quantum billiards.
- Subjects
GROUND state energy; COMPOSITION operators; SOBOLEV spaces; OPERATOR theory; QUANTUM states
- Publication
Journal of Mathematical Sciences, 2024, Vol 281, Issue 5, p677
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-024-07143-8