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

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
Journal	Journal of Mathematical Sciences
DOIs	https://doi.org/10.1007/s10958-022-06197-w
State	Accepted/In press - 1 Jan 2022

ASJC Scopus subject areas

Statistics and Probability
Mathematics (all)
Applied Mathematics

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title = "Estimates for Dirichlet Eigenvalues of Divergence Form Elliptic Operators in Non-Lipschitz Domains",

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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AU - Pchelintsev, V.

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AB - 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.

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

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