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arXiv · 2006.07009

Space quasiconformal composition operators with applications to Neumann eigenvalues

Vladimir Gol'dshtein·Ritva Hurri-Syrjänen·Valerii Pchelintsev·Alexander Ukhlov
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Abstract

In this article we obtain estimates of Neumann eigenvalues of $p$-Laplace operators in a large class of space domains satisfying quasihyperbolic boundary conditions. The suggested method is based on composition operators generated by quasiconformal mappings and their applications to Sobolev-Poincar\'e-inequalities. By using a sharp version of the inverse H\"older inequality we refine our estimates for quasi-balls, that is, images of balls under quasiconformal mappings of the whole space.

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Vladimir Gol'dshtein, Ritva Hurri-Syrjänen, Valerii Pchelintsev, Alexander Ukhlov. 2020-06-12. Space quasiconformal composition operators with applications to Neumann eigenvalues. https://arxiv.org/abs/2006.07009

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