The stickiness phenomena of nonlocal minimal surfaces: new results and a comparison with the classical case

Abstract

We discuss in this note the stickiness phenomena for nonlocal minimal surfaces. Classical minimal surfaces in convex domains do not stick to the boundary of the domain, hence examples of stickiness can be obtained only by removing the assumption of convexity. On the other hand, in the nonlocal framework, stickiness is ''generic''.  We provide various examples from the literature, and focus  on the case of complete stickiness in highly nonlocal regimes.