On compactness of one class of solutions of the Dirichlet problem
Complex Variables
2021-09-21 v1 Analysis of PDEs
Abstract
We consider the Dirichlet problem for the Beltrami equation in some simply connected domain. We consider the class of all homeomorphic solutions of such a problem with a normalization condition and set-theoretic constraints on their complex characteristics. We have proved the compactness of this class in terms of prime ends for an arbitrary continuous function in the Dirichlet condition.
Cite
@article{arxiv.2109.09197,
title = {On compactness of one class of solutions of the Dirichlet problem},
author = {Oleksandr Dovhopiatyi and Evgeny Sevost'yanov},
journal= {arXiv preprint arXiv:2109.09197},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2105.09373