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arXiv · 2009.06936

Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains

Vladimir Gol'dshtein·Valerii Pchelintsev·Alexander Ukhlov
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Abstract

We study spectral estimates of the divergence form uniform elliptic operators $-\textrm{div}[A(z) \nabla f(z)]$ with the Dirichlet boundary condition in bounded non-Lipschitz simply connected domains $Ω\subset \mathbb C$. The suggested method is based on the quasiconformal composition operators on Sobolev spaces with applications to the weighted Poincaré-Sobolev inequalities.

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Vladimir Gol'dshtein, Valerii Pchelintsev, Alexander Ukhlov. 2020-09-15. Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains. https://arxiv.org/abs/2009.06936

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