The stickiness property for antisymmetric nonlocal minimal graphs

TL;DR

This paper demonstrates that small antisymmetric perturbations can induce the stickiness phenomenon in nonlocal minimal graphs and establishes an odd symmetric maximum principle for these graphs.

Contribution

It introduces the effect of antisymmetric perturbations on nonlocal minimal graphs and proves an odd symmetric maximum principle, extending understanding of their boundary behavior.

Findings

Small antisymmetric perturbations cause stickiness in nonlocal minimal graphs.

An odd symmetric maximum principle for nonlocal minimal graphs is established.

Quantitative bounds are similar for symmetric and antisymmetric perturbations.

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.