Optimal gradient estimates for multi-phase integrals

TL;DR

This paper establishes precise reverse H"older inequalities for multi-phase variational integrals and uses these results to improve Calderón-Zygmund estimates in nonhomogeneous settings.

Contribution

It introduces sharp reverse H"older inequalities for multi-phase variational problems and applies them to enhance regularity estimates.

Findings

Proved sharp reverse H"older inequalities for multi-phase minima

Improved Calderón-Zygmund estimates for nonhomogeneous problems

Enhanced understanding of regularity in multi-phase variational integrals

Abstract

We prove sharp reverse H\"older inequalities for minima of multi-phase variational integrals and apply them to Calder\'on-Zygmund estimates for nonhomogeneous problems.