From the 1 of 6 linked papers with an AI index.
6 papers
The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and -solvability
Roberto Colombo, Xavier Fernández-Real, Xavier Ros-Oton
The paper develops a quantitative Dahlberg theory for the fractional Laplacian on bounded Lipschitz domains, proving reverse‑Hölder estimates for the s‑harmonic measure and establi…
Quantitative Local Convergence of Mean-Field Stein Variational Gradient Flow
Lénaïc Chizat, Maria Colombo, Roberto Colombo +1
Stein Variational Gradient Descent (SVGD) is a deterministic interacting-particle method for sampling from a target probability measure given access to its score function. In the m…
Quantitative Convergence of Wasserstein Gradient Flows of Kernel Mean Discrepancies
Lénaïc Chizat, Maria Colombo, Roberto Colombo +1
We study the quantitative convergence of Wasserstein gradient flows of Kernel Mean Discrepancy (KMD) (also known as Maximum Mean Discrepancy (MMD)) functionals. Our setting covers…
Sharpness of the Osgood Criterion for the Continuity Equation with Divergence-free Vector Fields
Roberto Colombo, Anuj Kumar
For any modulus of continuity that fails the Osgood condition, we construct a divergence-free velocity field for which the associated ODE admits at least tw…
A convex integration scheme for the continuity equation past the Sobolev embedding threshold
Maria Colombo, Roberto Colombo, Anuj Kumar
We introduce a convex integration scheme for the continuity equation in the context of the Di Perna-Lions theory that allows to build incompressible vector fields in $C_{t}W^{1,p}_…
Generic regularity of free boundaries in the obstacle problem for the fractional Laplacian
Matteo Carducci, Roberto Colombo
We establish generic regularity results of free boundaries for solutions of the obstacle problem for the fractional Laplacian . We prove that, for almost every obstacle, t…