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Article dans une revue

Flatness results for nonlocal minimal cones and subgraphs

Abstract : 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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https://hal-u-picardie.archives-ouvertes.fr/hal-03621410
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Soumis le : lundi 28 mars 2022 - 10:57:00
Dernière modification le : mardi 29 mars 2022 - 03:58:28

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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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