Quasiconformal mappings and Neumann eigenvalues of divergent elliptic operators

V. Gol'dshtein, V. Pchelintsev, A. Ukhlov

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1 Scopus citations


We study spectral properties of divergence form elliptic operators (Formula presented.) 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.

Original languageEnglish
JournalComplex Variables and Elliptic Equations
StateAccepted/In press - 1 Jan 2021


  • 30C62
  • 35J15
  • 46E35
  • Elliptic equations
  • Sobolev spaces
  • quasiconformal mappings


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