R. Colombo

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20242026

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Showing 2026 · math.APShow all

4 papers · 2 filters

math.AP2026

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 $R^{n + 1} \times R$ , which models the melting of a thin sheet of ice over…

math.AP2026

The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and $L^{2}$ -solvability

Roberto Colombo, Xavier Fernández-Real, Xavier Ros-Oton

Given $s \in (0, 1)$ and a bounded Lipschitz domain $Ω \subset R^{n}$ , we establish a quantitative Dahlberg theory for the $s$ -harmonic measure of $Ω$ , $ω_{s}^{x}$ . In the nonloc…

math.AP2026

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…

math.AP2026

Sharpness of the Osgood Criterion for the Continuity Equation with Divergence-free Vector Fields

Roberto Colombo, Anuj Kumar

For any modulus of continuity $ω$ that fails the Osgood condition, we construct a divergence-free velocity field $v \in C_{t} C_{x}^{ω}$ for which the associated ODE admits at least two…

The singular set in the thin Stefan problem

The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and L2-solvability

Quantitative Convergence of Wasserstein Gradient Flows of Kernel Mean Discrepancies

Sharpness of the Osgood Criterion for the Continuity Equation with Divergence-free Vector Fields

The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and $L^{2}$ -solvability