On Beltrami equations with the inverse conditions and hydrodynamic normalization

TL;DR

This paper investigates the existence and convergence of solutions to Beltrami equations with hydrodynamic normalization, focusing on inverse conditions and their behavior in the complex plane.

Contribution

It establishes the existence of solutions under inverse dilation conditions within Sobolev mappings and analyzes their local uniform convergence.

Findings

Existence of solutions with hydrodynamic normalization under inverse dilation conditions

Convergence results for sequences of solutions in the complex plane

Solutions belong to the class of continuous Sobolev mappings

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.