- 15-51 Serena Dipierro, Ovidiu Savin and Enrico Valdinoci
- Graph properties for nonlocal minimal surfaces
Jun 13, 15
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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
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.