6 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 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…
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, th…