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arXiv · 2109.09197

On compactness of one class of solutions of the Dirichlet problem

Oleksandr Dovhopiatyi·Evgeny Sevost'yanov
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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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Oleksandr Dovhopiatyi, Evgeny Sevost'yanov. 2021-09-19. On compactness of one class of solutions of the Dirichlet problem. https://arxiv.org/abs/2109.09197

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