Calculus of Variations and Geometric Measure Theory

M. G. Mora

Local calibrations for minimizers of the Mumford-Shah functional with a triple junction

created on 11 May 2001
modified on 30 Jul 2002


Published Paper

Inserted: 11 may 2001
Last Updated: 30 jul 2002

Journal: Communications in Contemporary Mathematics
Volume: 4
Number: 2
Pages: 297-326
Year: 2002


We prove that, if $u$ is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of $u$ is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood $U$ of the origin such that $u$ is a minimizer of the Mumford-Shah functional on $U$ with respect to its own boundary conditions on $\partial U$. The proof is obtained by using the calibration method.

Keywords: free discontinuity problems, Mumford-Shah functional, calibration method