On Beltrami equations with the inverse conditions and hydrodynamic normalization

2022/03/04 by Sevost'yanov, Evgeny, Dovhopiatyi, Oleksandr
#30C65 #30L10 #31A15 #31A20 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.02562

Abstract

We consider problems concerning the existence of solutions of the Beltrami equations and their convergence in the entire complex plane. We are mainly interested in the case when these solutions satisfy the so-called hydrodynamic normalization condition in the neighborhood of infinity. Under conditions related to dilations of inverse mappings, we have established the existence of such solutions in the class of continuous Sobolev mappings. We have also obtained results on the locally uniform limit of a sequence of such solutions.

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