Serena Dipierro, Ovidiu Savin and Enrico Valdinoci
Graph properties for nonlocal minimal surfaces
(500K, pdf)

ABSTRACT.  In this paper we show that a nonlocal minimal surface which is 
a graph outside a cylinder is in fact a graph in the whole of the space. 
As a consequence, in dimension~$3$, we show that the graph 
is smooth. 
The proofs rely on convolution techniques 
and appropriate integral estimates which show the pointwise 
validity of an Euler-Lagrange equation related to the nonlocal mean curvature.