Higher integrability of the gradient for minimizers of the 2d Mumford–Shah energy

We prove the existence of an exponent p>2 with the property that the approximate gradient of any local minimizer of the 2-dimensional Mumford–Shah energy belongs to .

RésuméOn démontre lʼéxistence dʼun exposant p>2 tel que le gradient approche dʼune fonction 2-dimensionelle quelconque qui minimise localement lʼénergie de Mumford–Shah appartient à lʼèspace .