Quasiconformal mappings and Neumann eigenvalues of divergent elliptic operators. (English) Zbl 1495.35131
Summary: We study spectral properties of divergence form elliptic operators \(-\operatorname{div}[A(z) \nabla f(z)]\) 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.
MSC:
| 35P05 | General topics in linear spectral theory for PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 30C62 | Quasiconformal mappings in the complex plane |
Keywords:
elliptic equations; Sobolev spaces; quasiconformal mappings; quasihyperbolic boundary conditionsReferences:
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