Minimizing movements of the Mumford and Shah energy

Antonin Chambolle; Francesco Doveri

doi:10.3934/dcds.1997.3.153

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1997, Volume 3, Issue 2: 153-174. Doi: 10.3934/dcds.1997.3.153

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Minimizing movements of the Mumford and Shah energy

Antonin Chambolle^1, and
Francesco Doveri^2,

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

Received: September 30, 1996

Published: March 1997

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Abstract

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.

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Mathematics Subject Classification: 35K20, 49M10, 49Q20, 73M25.

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