# Local regularity for fractional heat equations

## TL;DR

This paper establishes the maximal local regularity of weak solutions to fractional heat equations with Dirichlet boundary conditions on arbitrary bounded domains, combining classical and new local regularity results.

## Contribution

It introduces new local regularity results for elliptic problems associated with fractional Laplacians and applies them to prove maximal local regularity for fractional heat equations.

## Key findings

- Proves maximal local regularity for solutions to fractional heat equations.
- Develops new local regularity results for associated elliptic problems.
- Combines classical and novel techniques for regularity analysis.

## Abstract

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.