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

Vladimir Gol'dshtein; Valerii Pchelintsev; Alexander Ukhlov

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

Analysis of PDEs 2020-09-16 v1

Authors: Vladimir Gol'dshtein , Valerii Pchelintsev , Alexander Ukhlov

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 $\Omega \subset \mathbb C$ . The suggested method is based on the quasiconformal composition operators on Sobolev spaces with applications to the weighted Poincar\'e-Sobolev inequalities.

Keywords

dirichlet eigenvalues divergent elliptic operators non-lipschitz domains quasiconformal composition operators sobolev spaces weighted poincaré-sobolev inequalities

Cite

@article{arxiv.2009.06936,
  title  = {Estimates of Dirichlet eigenvalues of divergent elliptic operators in non-Lipschitz domains},
  author = {Vladimir Gol'dshtein and Valerii Pchelintsev and Alexander Ukhlov},
  journal= {arXiv preprint arXiv:2009.06936},
  year   = {2020}
}

Comments

13 pages

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