# American Institute of Mathematical Sciences

April  1997, 3(2): 153-174. doi: 10.3934/dcds.1997.3.153

## Minimizing movements of the Mumford and Shah energy

 1 CEREMADE (CNRS URA 749), Université de Paris-Dauphine, 75775 Paris CEDEX 16, France 2 SISSA, Via Beirut 2-4, 34013 Trieste, Italy

Received  October 1996 Published  January 1997

We study a simplified model of fracture propagation introduced by L. Ambrosio and A. Braides, based on the evolution by minimizing movements of the Mumford-Shah energy. In the two-dimensional case, we show that under a few additional assumptions on the "fracture" the movement solves the heat equation, with (weak) Neumann boundary conditions, and we are able to give some estimate on the decrease of the Mumford-Shah energy.
Citation: Antonin Chambolle, Francesco Doveri. Minimizing movements of the Mumford and Shah energy. Discrete and Continuous Dynamical Systems, 1997, 3 (2) : 153-174. doi: 10.3934/dcds.1997.3.153
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