Nonlocal minimal surfaces (Viscosity Solutions of Differential Equations and Related Topics)
Jean‐Michel Roquejoffre · Institutional Repositories DataBase (IRDB) · 2010
This paper describes a joint work with L. Caffarelli and O. Savin.We introduce a new notion of minimal surfaces, replacing the $BV$ norm by the $H^{\alpha}$ one, with $\alpha<\frac{1}{2}$ .The resulting sets are called $\alpha$ -minimal sets.The main result is a de Giorgi type theorem: if an $\alpha$ -minimal set is flat enough, then it is smooth.