On compactness of one class of solutions of the Dirichlet problem

2021/09/19 by Dovhopiatyi, Oleksandr, Sevost'yanov, Evgeny
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.09197

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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