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…
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…
Beurling-Deny formula for Sobolev-Bregman forms
Michał Gutowski, Mateusz Kwaśnicki
For an arbitrary regular Dirichlet form and the associated symmetric Markovian semigroup , we consider the corresponding Sobolev-Bregman form $\mathscr{E}_p(u) =…
Simplicity of eigenvalues of the fractional Laplace operator in an interval
Mateusz Kwaśnicki
We give a short proof of simplicity of the eigenvalues of the fractional Laplace operator in an interval, a result shown recently by Fall, Ghimenti, Micheletti and Pistoia [Calc. V…