A note on the dimension of the singular set in free interface problems

Alessio Figalli; Guido De Philippis

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A note on the dimension of the singular set in free interface problems

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arxiv 1405.7827 v1 pith:FSM5KA4D submitted 2014-05-30 math.AP

Guido De Philippis , Alessio Figalli This is my paper

classification math.AP

keywords singularfreeinterfacenoteproblemsclasscorollarydimension

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abstract

The aim of this note is to investigate the size of the singular set of a general class of free interface problems. We show porosity of the singular set, obtaining as a corollary that both its Hausdorff and Minkowski dimensions are strictly smaller than $n-1$.

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