Graph properties for nonlocal minimal surfaces
- Dipierro, Serena
- Savin, Ovidiu
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 49Q05 35R11 53A10
- Nonlocal minimal surfaces, graph properties, regularity theory
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.
- Calc. Var. Partial Differ. Equ., 55 (2016) pp. 86/1--86/25.