Publications de Xavier Fernandez-Real Girona

Publications associées (15)

Iron status influences non-alcoholic fatty liver disease in obesity through the gut microbiome

Background: The gut microbiome and iron status are known to play a role in the pathophysiology of nonalcoholic fatty liver disease (NAFLD), although their complex interaction remains unclear. Results: Here, we applied an integrative systems medicine approa ...

2021

Obesity Impairs Short-Term and Working Memory through Gut Microbial Metabolism of Aromatic Amino Acids

Xavier Fernandez-Real Girona

The gut microbiome has been linked to fear extinction learning in animal models. Here, we aimed to explore the gut microbiome and memory domains according to obesity status. A specific microbiome profile associated with short-term memory, working memory, a ...

Cell Press2020

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Xavier Fernandez-Real Girona

We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

Free Boundary Regularity for Almost Every Solution to the Signorini Problem

Xavier Fernandez-Real Girona

We investigate the regularity of the free boundary for the Signorini problem in Rn+1. It is known that regular points are (n−1)-dimensional and C∞. However, even for C∞ obstacles φ, the set of non-regular (or degenerate) points could be very large—e.g. wit ...

2021

Regularity for the Boltzmann Equation Conditional to Pressure and Moment Bounds

Xavier Fernandez-Real Girona

We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in

L^\infty

in the case of hard potentials. As a consequence, we derive $C^{\i ...

Springer Science and Business Media LLC2025

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Xavier Fernandez-Real Girona, Riccardo Tione

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

American Mathematical Society (AMS)2023

Infinite-width limit of deep linear neural networks

Maria Colombo, Xavier Fernandez-Real Girona, Lénaïc Chizat

This paper studies the infinite-width limit of deep linear neural networks (NNs) initialized with random parameters. We obtain that, when the number of parameters diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a ...

Hoboken2024

Generic regularity of free boundaries for the thin obstacle problem

Xavier Fernandez-Real Girona

The free boundary for the Signorini problem in Rn+1 is smooth outside of a degenerate set, which can have the same dimension (n - 1) as the free boundary itself. In [15] it was shown that generically, the set where the free boundary is not smooth is at mos ...

Academic Press Inc Elsevier Science2023

Stable cones in the thin one-phase problem

Xavier Fernandez-Real Girona

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Johns Hopkins Univ Press2024

Continuity up to the boundary for minimizers of the one-phase Bernoulli problem

Xavier Fernandez-Real Girona

We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and Hölder-continuous boundary data. As an application, we use them to extend recen ...

Springer Science and Business Media LLC2025

Graphical solutions to one-phase free boundary problems

Xavier Fernandez-Real Girona

We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...

Walter De Gruyter Gmbh2023

SMOOTH APPROXIMATIONS FOR FULLY NONLINEAR NONLOCAL ELLIPTIC EQUATIONS

Xavier Fernandez-Real Girona

We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth (C infinity) solutions. ...

Amer Mathematical Soc2023

Integro-Differential Elliptic Equations

Xavier Fernandez-Real Girona

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathemat ...

Birkhauser2024

Obesity-associated deficits in inhibitory control are phenocopied to mice through gut microbiota changes in one-carbon and aromatic amino acids metabolic pathways

Xavier Fernandez-Real Girona

Background Inhibitory control (IC) is critical to keep long-term goals in everyday life. Bidirectional relationships between IC deficits and obesity are behind unhealthy eating and physical exercise habits. ...

BMJ PUBLISHING GROUP2021

Optimal regularity for the fully nonlinear thin obstacle problem

Maria Colombo, Xavier Fernandez-Real Girona

In this work, we establish the optimal regularity for solutions to the fully nonlinear thin obstacle problem. In particular, we show the existence of an optimal exponent αF such that u is C1,αF on either side of the obstacle. In order to do that, we prove ...

2025