Calculus of Variations and Geometric Measure Theory

A. Chambolle - M. Goldman - M. Novaga

Existence and qualitative properties of isoperimetric sets in periodic media

created by goldman on 07 Nov 2012
modified by novaga on 15 May 2016


Published Paper

Inserted: 7 nov 2012
Last Updated: 15 may 2016

Journal: in Geometric Partial Differential Equations, Edizioni della Normale, CRM Series
Volume: 15
Pages: 93-104
Year: 2013


We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension, also known as stable norm (or minimal action) in Weak KAM theory. In particular we investigate its strict convexity and differentiability properties.