Calculus of Variations and Geometric Measure Theory

G. De Philippis - A. Figalli

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

created by dephilipp on 27 May 2014
modified on 30 Oct 2017


Accepted Paper

Inserted: 27 may 2014
Last Updated: 30 oct 2017

Journal: Differential Integral Equations
Year: 2014

ArXiv: 1405.7827 PDF


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 $n-1$.