Calculus of Variations and Geometric Measure Theory

C. De Lellis - M. Focardi

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

created by focardi on 20 Feb 2012
modified on 06 Nov 2013


Published Paper

Inserted: 20 feb 2012
Last Updated: 6 nov 2013

Journal: J. Math. Pures Appl.
Volume: 100
Pages: 391-409
Year: 2013


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 $L^p_{loc}$.

Keywords: Local minimizer, higher integrability, Mumford-Shah energy, Caccioppoli partition