Space quasiconformal composition operators with applications to Neumann eigenvalues
Analysis of PDEs
2020-08-26 v2
Abstract
In this article we obtain estimates of Neumann eigenvalues of -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.
Cite
@article{arxiv.2006.07009,
title = {Space quasiconformal composition operators with applications to Neumann eigenvalues},
author = {Vladimir Gol'dshtein and Ritva Hurri-Syrjänen and Valerii Pchelintsev and Alexander Ukhlov},
journal= {arXiv preprint arXiv:2006.07009},
year = {2020}
}
Comments
16 pages