4 papers
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. Our results hold for general s…
Poisson kernels on the half-plane are bell-shaped
Mateusz Kwaśnicki
Consider a second-order elliptic operator in the half-plane with coefficients depending only on the second coordinate. The Poisson kernel for …
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…
Harmonic extension technique: probabilistic and analytic perspectives
Mateusz Kwaśnicki
Consider a path of the reflected Brownian motion in the half-plane , and erase its part contained in the interior . What is left is, in an appropriate sense…