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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.

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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