Estimates for Dirichlet Eigenvalues of Divergence Form Elliptic Operators in Non-Lipschitz Domains

V. Gol’dshtein; V. Pchelintsev; A. Ukhlov

doi:10.1007/s10958-022-06197-w

Estimates for Dirichlet Eigenvalues of Divergence Form Elliptic Operators in Non-Lipschitz Domains

V. Gol’dshtein, V. Pchelintsev, A. Ukhlov

Department of Mathematics

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

1 Scopus citations

Abstract

We obtain estimates for Dirichlet eigenvalues of divergence form elliptic operators −div [A(z)∇f(z)] in bounded non-Lipschitz domains. We propose a method based on the quasiconformal composition operators on Sobolev spaces with application to weighted Poincaré–Sobolev inequalities.

Original language	English
Pages (from-to)	343-354
Number of pages	12
Journal	Journal of Mathematical Sciences
Volume	268
Issue number	3
DOIs	https://doi.org/10.1007/s10958-022-06197-w
State	Published - 1 Dec 2022

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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abstract = "We obtain estimates for Dirichlet eigenvalues of divergence form elliptic operators −div [A(z)∇f(z)] in bounded non-Lipschitz domains. We propose a method based on the quasiconformal composition operators on Sobolev spaces with application to weighted Poincar{\'e}–Sobolev inequalities.",

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Estimates for Dirichlet Eigenvalues of Divergence Form Elliptic Operators in Non-Lipschitz Domains

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