On integral conditions for the general Beltrami equations

TL;DR

This paper establishes existence theorems for degenerate Beltrami equations under integral restrictions on dilatations, with implications for mathematical physics and related applications.

Contribution

It introduces new existence results for Beltrami equations with integral conditions, including second type and reduced forms, expanding their theoretical understanding.

Findings

Existence theorems for degenerate Beltrami equations

Applicability to equations in mathematical physics

Results under integral restrictions on dilatations

Abstract

Under integral restrictions on dilatations, it is proved existence theorems for the degenerate Beltrami equations with two characteristics and, in particular, to the Beltrami equations of the second type that play a great role in many problems of mathematical physics and to the so--called reduced Beltrami equations that also have significant applications.