Gradient $L^q$ theory for a class of nondiagonal elliptic systems

TL;DR

This paper improves the $L^q$ regularity theory for a class of nondiagonal elliptic systems with $p$-growth by leveraging recent results on their Hölder continuity.

Contribution

It introduces an enhanced $L^q$ theory for nondiagonal elliptic systems, building upon recent Hölder continuity results.

Findings

Improved $L^q$ regularity results for elliptic systems.

Application of Hölder continuity to $L^q$ theory.

Extension of regularity theory for systems with $p$-growth.

Abstract

We show that the new result on H\"older continuity of solutions to a class of nondiagonal elliptic systems with $p$-growth in [2] can be used to improve the $L^q$ theory for such systems.