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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2019

Flatness results for nonlocal minimal cones and subgraphs

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Résumé

We show that nonlocal minimal cones which are non-singular sub-graphs outside the origin are necessarily halfspaces. The proof is based on classical ideas of [14] and on the computation of the linearized nonlocal mean curvature operator, which is proved to satisfy a suitable maximum principle. With this, we obtain new, and somehow simpler, proofs of the Bernstein-type results for nonlocal minimal surfaces which have been recently established in [20]. In addition, we establish a new nonlocal Bernstein-Moser-type result which classifies Lipschitz nonlocal minimal subgraphs outside a ball.
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Dates et versions

hal-03621410 , version 1 (28-03-2022)

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  • HAL Id : hal-03621410 , version 1

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Alberto Farina, Enrico Valdinoci. Flatness results for nonlocal minimal cones and subgraphs. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2019, 19 (4), pp.1281-1301. ⟨hal-03621410⟩
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