5 papers · 1 filter
Volumetric density estimates for nonlocal minimal surfaces
Mateusz Kwaśnicki, Jack Thompson
In this article, we prove that viscosity subsolutions to nonlocal mean curvature-type equations satisfy universal volumetric estimates at all scales provided their boundary has zer…
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.
The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
Serena Dipierro, Mateusz Kwaśnicki, 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…
Quantitative stability for the nonlocal overdetermined Serrin problem
Serena Dipierro, Giorgio Poggesi, Jack Thompson +1
We establish quantitative stability for the nonlocal Serrin overdetermined problem, via the method of the moving planes. Interestingly, our stability estimate is even better than t…
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…