Quasiconformal Mappings and Neumann Eigenvalues of Divergent Elliptic Operators

Vladimir Gol'dshtein; Valeryi Pchelintsev; Alexander Ukhlov

Quasiconformal Mappings and Neumann Eigenvalues of Divergent Elliptic Operators

Analysis of PDEs 2020-04-24 v2

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

Abstract

We study spectral properties of divergence form elliptic operators $-\textrm{div} [A(z) \nabla f(z)]$ with the Neumann boundary condition in planar domains (including some fractal type domains), that satisfy to the quasihyperbolic boundary conditions. Our method is based on an interplay between quasiconformal mappings, elliptic operators and composition operators on Sobolev spaces.

Keywords

quasiconformal mappings Neumann eigenvalues divergent elliptic operators Sobolev spaces planar domains quasihyperbolic boundary conditions

Cite

@article{arxiv.1903.11301,
  title  = {Quasiconformal Mappings and Neumann Eigenvalues of Divergent Elliptic Operators},
  author = {Vladimir Gol'dshtein and Valeryi Pchelintsev and Alexander Ukhlov},
  journal= {arXiv preprint arXiv:1903.11301},
  year   = {2020}
}

Comments

21 pages

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