The stickiness property for antisymmetric nonlocal minimal graphs

Abstract

We show that arbitrarily small antisymmetric perturbations of the zero function are sufficient to produce the stickiness phenomenon for planar nonlocal minimal graphs (with the same quantitative bounds obtained for the case of even symmetric perturbations, up to multiplicative constants).In proving this result, one also establishes an odd symmetric version of the maximum principle for nonlocal minimal graphs, according to which the odd symmetric minimizer is positive in the direction of the positive bump and negative in the direction of the negative bump. 2020 Mathematics Subject Classification. 35R11, 49Q05. Key words and phrases. Nonlocal minimal surfaces, stickiness, qualitative and quantitative behavior. S. Dipierro and E. Valdinoci are members of AustMS. S. Dipierro is supported by the Australian Research Council DECRA DE180100957 "PDEs, free boundaries and applications". E. Valdinoci is supported by the Australian Laureate Fellowship FL190100081 "Minimal surfaces, free boundaries and partial differential equations".