works on
boundary value problems 1dahlberg theorem 1fractional laplacian 1lipschitz domains 1nonlocal operators 1

From the 1 of 14 linked papers with an AI index.

collaborators

14 papers

math.AP2026

Superharmonicity of the fractional ground state

Nicola De Nitti, Xavier Fernández-Real

Let . We prove that the positive ground state of the fractional Laplacian on an arbitrary open set , whenever it exists, satisfies in…

math.AP2026

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…

math.AP2026

Nonlocal minimal surfaces are generically unique, and smooth in one extra dimension

Serena Dipierro, Xavier Fernández-Real, Enrico Valdinoci

We study the fractional Plateau problem for -minimal sets with prescribed exterior datum. For fixed exterior data, minimizers need not be unique, and singularities may occur bey…

math.AP2026

Classification of blow-ups for the Alt--Phillips problem in three dimensions

Xavier Fernández-Real

We prove a flatness theorem for classical stable homogeneous solutions of the -Alt--Phillips free boundary problem in three dimensions in the range , where is…

math.DG2026

Improvement of flatness in annuli

Xavier Fernández-Real, Enric Florit-Simon, Joaquim Serra

We present a short and flexible improvement-of-flatness argument adapted to the setting of exterior domains, where one is naturally led to work with annuli instead of balls. As a m…

stat.ML2026

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…