WIAS Preprint No. 2131, (2015)

Graph properties for nonlocal minimal surfaces


  • Dipierro, Serena
  • Savin, Ovidiu
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

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.

Appeared in

  • Calc. Var. Partial Differ. Equ., 55 (2016) pp. 86/1--86/25.

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