November 9, 2021

The Stickiness Property of Nonlocal Minimal Surfaces

Surfaces that minimize a nonlocal perimeter functional exhibit quite different behaviors than the ones minimizing the classical perimeter. Among these peculiar features, an interesting property, which is also in contrast with the pattern produced by the solutions of linear equations, is given by the capacity, and the strong tendency, of adhering at the boundary. We will discuss this phenomenon and present some recent results.