Self-improving properties of very weak solutions to double phase systems

TL;DR

This paper demonstrates that very weak solutions to certain complex elliptic systems naturally improve their regularity under specific conditions, revealing intrinsic self-improving properties of these mathematical solutions.

Contribution

It establishes the self-improving property for very weak solutions to double phase elliptic systems under optimal assumptions, advancing understanding of their regularity behavior.

Findings

Self-improving regularity of solutions proven

Optimal conditions identified for regularity enhancement

Advances understanding of double phase elliptic systems

Abstract

We prove the self-improving property of very weak solutions to non-uniformly elliptic problems of double phase type in divergence form under sharp assumptions on the nonlinearity.