Calculus of Variations and Geometric Measure Theory

C. De Lellis - M. Focardi

Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy

created by focardi on 02 Apr 2012
modified on 06 Nov 2013


Published Paper

Inserted: 2 apr 2012
Last Updated: 6 nov 2013

Journal: Manuscripta Math.
Volume: 132
Pages: 215-232
Year: 2013
Doi: 10.1007/s00229-012-0601-y


We prove, using direct variational arguments, an explicit energy-treshold criterion for regular points of 2-dimensional Mumford-Shah energy (quasi-)minimizers. From this we infer an explicit constant for the density lower bound of De Giorgi, Carriero and Leaci.

Keywords: Local minimizer, Mumford-Shah energy, Density lower bound