On the Homogeneity of Global Minimizers for the Mumford-Shah Functional when is a Smooth Cone

  • Antoine Lemenant

    Université Paris XI Paris-Sud, Orsay, France

Abstract

We show that if is a global minimizer for the Mumford–Shah functional in , and if is a smooth enough cone, then (modulo constants) is a homogenous function of degree . We deduce some applications in as for instance that an angular sector cannot be the singular set of a global minimizer, that if is a half-plane then is the corresponding cracktip function of two variables, or that if is a cone that meets with an union of curvilinear convex polygones, then it is a , or .

Cite this article

Antoine Lemenant, On the Homogeneity of Global Minimizers for the Mumford-Shah Functional when is a Smooth Cone. Rend. Sem. Mat. Univ. Padova 122 (2009), pp. 129–159

DOI 10.4171/RSMUP/122-9