5 papers · 1 filter
The singular set in the thin Stefan problem
Matteo Carducci, Roberto Colombo, Clara Torres-Latorre
We study the singular set of the free boundary for solutions of the thin Stefan problem in , which models the melting of a thin sheet of ice over…
The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and -solvability
Roberto Colombo, Xavier Fernández-Real, Xavier Ros-Oton
Given and a bounded Lipschitz domain , we establish a quantitative Dahlberg theory for the -harmonic measure of , . In the nonloc…
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 two…