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

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

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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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-12, Vol.268 (3), p.343-354
Hauptverfasser: Gol’dshtein, V., Pchelintsev, V., Ukhlov, A.
Format: Artikel
Sprache:eng
Schlagworte:
Dirichlet problem
Domains
Eigenvalues
Estimates
Mathematics
Mathematics and Statistics
Operators
Sobolev space
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Zusammenfassung: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06197-w