On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
نویسنده
چکیده
We show that if (u,K) is a global minimizer for the Mumford-Shah functional in R , and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1 2 . We deduce some applications in R as for instance that an angular sector cannot be the singular set of a global minimizer, that if K is a half-plane then u is the corresponding cracktip function of two variables, or that if K is a cone that meets S with an union of C∞ curvilinear convex polygones, then it is a P, Y or T.
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