Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators

Vladimir Gol'dshtein; Valerii Pchelintsev; Alexander Ukhlov

Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators

Analysis of PDEs 2019-05-15 v1

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

Abstract

We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Dirichlet boundary condition in non-Lipschitz domains $\widetilde{\Omega} \subset \mathbb C$ . The suggested method is based on connections of planar quasiconformal mappings with Sobolev spaces and its applications to the Poincar\'e inequalities.

Keywords

spectral stability estimates divergence form elliptic operators dirichlet boundary condition non-lipschitz domains quasiconformal mappings sobolev spaces poincare inequalities

Cite

@article{arxiv.1905.05473,
  title  = {Spectral Stability Estimates of Dirichlet Divergence Form Elliptic Operators},
  author = {Vladimir Gol'dshtein and Valerii Pchelintsev and Alexander Ukhlov},
  journal= {arXiv preprint arXiv:1905.05473},
  year   = {2019}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:1903.11301

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