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Minimizing movements of the Mumford and Shah energy

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

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