On a variational method for the Beltrami equations

TL;DR

This paper develops a variational approach for solving degenerate Beltrami equations with set-theoretic restrictions on the complex coefficient, establishing maximum principles and extremum conditions.

Contribution

It introduces a novel variational method for regular solutions to degenerate Beltrami equations with set-theoretic coefficient restrictions.

Findings

Proved the variational maximum principle.

Derived necessary conditions of extremum.

Constructed variations for solution classes.

Abstract

We construct variations for the classes of regular solutions to degenerate Beltrami equations with restrictions of the set-theoretic type for the complex coefficient. On this basis, we prove the variational maximum principle and other necessary conditions of extremum.