Spectral Estimates of the Dirichlet-Laplace Operator in Conformal Regular Domains

Ivan Kolesnikov; Valerii Pchelintsev

doi:10.1007/s10958-024-07143-8

Spectral Estimates of the Dirichlet-Laplace Operator in Conformal Regular Domains

Ivan Kolesnikov
, Valerii Pchelintsev

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	677-691
Number of pages	15
Journal	Journal of Mathematical Sciences (United States)
Volume	281
Issue number	5
DOIs	https://doi.org/10.1007/s10958-024-07143-8
State	Published - 1 Jun 2024
Externally published	Yes

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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10.1007/s10958-024-07143-8

Cite this

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abstract = "We consider conformal spectral estimates of the Dirichlet{\textendash}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 Poincar{\'e}-Sobolev inequalities. We obtain lower estimates for the first eigenvalue of the Dirichlet{\textendash}Laplace operator in the class of conformal regular domains and conformal estimates for the ground state energy of quantum billiards.",

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PY - 2024/6/1

Y1 - 2024/6/1

N2 - 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.

AB - 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.

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Spectral Estimates of the Dirichlet-Laplace Operator in Conformal Regular Domains

Abstract

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