# On the existence of a solution of the Beltrami equation with degeneration

## TL;DR

This paper identifies conditions under which the degenerate Beltrami equation admits a continuous Sobolev-class solution, and shows that with extra conditions, this solution can be homeomorphic.

## Contribution

It provides new criteria for the existence of solutions to the degenerate Beltrami equation and establishes conditions for the solution to be homeomorphic.

## Key findings

- Conditions for existence of Sobolev-class solutions
- Additional requirements ensure solutions are homeomorphic
- Extension of solutions to degenerate elliptic cases

## Abstract

We have found one of the possible conditions under which the Beltrami equation with degeneration of ellipticity has a continuous solution of the Sobolev class. With some additional requirements, this solution is homeomorphic