We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter s when s → 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.
Regularity properties of nonlocal minimal surfaces via limiting arguments / L. Caffarelli, E. Valdinoci. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 248(2013), pp. 843-871.
Regularity properties of nonlocal minimal surfaces via limiting arguments
E. Valdinoci
2013
Abstract
We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter s when s → 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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