11-69 Luis Caffarelli, Enrico Valdinoci

Regularity properties of nonlocal minimal surfaces via limiting arguments (372K, LaTeX) May 5, 11

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Abstract. We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter~$s$ when~$s ightarrow 1^-$. As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the nonlocal minimal surfaces are smooth when the dimension of the ambient space is less or equal than~$7$ and~$s$ is close to~$1$.

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