Abstract
Abstract We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi [6] stating that the validity of Bernstein’s theorem in dimension n + 1 {n+1} is a consequence of the nonexistence of n-dimensional singular minimal cones in ℝ n {\mathbb{R}^{n}} .
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