# A priori estimates and theory of existence for parabolic equations in variable H\"older spaces

## TL;DR

This paper develops a theoretical framework for parabolic equations within variable H"older spaces, establishing existence and uniqueness of solutions on Euclidean domains, thus advancing the mathematical understanding of such equations.

## Contribution

It introduces a priori estimates and proves the existence and uniqueness of solutions for parabolic equations in variable H"older spaces, a novel extension of classical theory.

## Key findings

- Existence and uniqueness of solutions established.
- A priori estimates derived for solutions.
- Extension of classical parabolic theory to variable H"older spaces.

## Abstract

We study parabolic equations in variable H\"older spaces on domains of Euclidean spaces. The existence and uniqueness of solutions is proved.