TY - JOUR
T1 - Flatness results for nonlocal minimal cones and subgraphs
AU - Farina, Alberto
AU - Valdinoci, Enrico
PY - 2019
Y1 - 2019
N2 - We show that nonlocal minimal cones which are non-singular subgraphs 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.
AB - We show that nonlocal minimal cones which are non-singular subgraphs 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.
UR - http://www.scopus.com/inward/record.url?scp=85080884013&partnerID=8YFLogxK
U2 - 10.2422/2036-2145.201708_019
DO - 10.2422/2036-2145.201708_019
M3 - Article
AN - SCOPUS:85080884013
VL - 19
SP - 1281
EP - 1301
JO - Annali della Scuola Normale Superiore di Pisa: Classe di Scienze
JF - Annali della Scuola Normale Superiore di Pisa: Classe di Scienze
SN - 0391-173X
IS - 4
ER -