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Analysis
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Camillo De Lellis, Zoom (details in announcement email): The regularity theory for the Mumford-Shah functional
Wednesday, March 31, 2021, 01:00pm - 02:00pm
In 1989 Mumford and Shah proposed a simple minimization problem in the plane: among functions which, roughly speaking, are piecewise smooth and undergo jump discontinuities on a set of finite length, one seeks those which minimize the sum of the length of the set of discontinuities and of the Dirichlet energy. A rich and successful theory was developed in the late eighties and in the nineties to deal with this and similar variational problems. However the main conjecture of Mumford and Shah, which details how regular a minimizer is expected to be, is still widely open. I will give an overview of the ideas in the existence theory and I will survey the regularity theorems proved in the literature in the past three decades, arriving to a recent joint work of mine with Matteo Focardi and Silvia Ghinassi.
Location: Zoom (details in announcement email)

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