4 papers
Volumetric density estimates for nonlocal minimal surfaces
Mateusz KwaÅnicki, Jack Thompson
In this article, we prove that viscosity subsolutions to nonlocal mean curvature-type equations satisfy universal volumetric estimates at all scales. Our results hold for general s…
A half-space theorem for nonlocal minimal surfaces
Matteo Cozzi, Jack Thompson
We establish a half-space theorem à la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.
Some nonlocal formulas inspired by an identity of James Simon
Serena Dipierro, Jack Thompson, Enrico Valdinoci
Inspired by a classical identity proved by James Simons, we establish a new geometric formula in a nonlocal, possibly fractional, setting. Our formula also recovers the classical c…
The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
Serena Dipierro, Mateusz KwaÅnicki, Jack Thompson +1
We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic opera…