Higher integrability for minimizers of the Mumford-Shah functional

TL;DR

This paper proves that the gradient of local minimizers of the Mumford-Shah functional has higher integrability, confirming a longstanding conjecture by De Giorgi and advancing understanding of this variational problem.

Contribution

It establishes higher integrability for the gradient of minimizers of the Mumford-Shah functional, solving De Giorgi's conjecture.

Findings

Proves higher integrability for the gradient of minimizers.

Confirms De Giorgi's conjecture.

Advances theoretical understanding of Mumford-Shah minimizers.

Abstract

We prove higher integrability for the gradient of local minimizers of the Mumford-Shah energy functional, providing a positive answer to a conjecture of De Giorgi.