On the $C^1$ regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients

TL;DR

This paper proves that solutions to divergence form elliptic systems with Dini-continuous coefficients are continuously differentiable, advancing understanding of regularity conditions for such systems.

Contribution

It establishes $C^1$ regularity for elliptic systems under Dini-continuous coefficients, a significant extension beyond previously known regularity results.

Findings

Solutions are $C^1$ continuous under Dini-continuous coefficients

Extends regularity theory for elliptic systems

Provides new techniques for handling Dini continuity

Abstract

We prove $C^1$ regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients