We show that the only nonlocal s-minimal cones in ℝ2 are the trivial ones for all S ∈ (0, 1). As a consequence we obtain that the singular set of a nonlocal minimal surface has at most n - 3 Hausdorff dimension.
Regularity of nonlocal minimal cones in dimension 2 / O. Savin, E. Valdinoci. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 48:1-2(2013), pp. 33-39.
Regularity of nonlocal minimal cones in dimension 2
E. Valdinoci
2013
Abstract
We show that the only nonlocal s-minimal cones in ℝ2 are the trivial ones for all S ∈ (0, 1). As a consequence we obtain that the singular set of a nonlocal minimal surface has at most n - 3 Hausdorff dimension.
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