Personne
Xavier Fernandez-Real Girona
Publications associées (9)
Stable cones in the thin one-phase problem
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 Press2024IMPROVED 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 ...
Providence2023Graphical solutions to one-phase free boundary problems
Xavier Fernandez-Real Girona, Hui Yu
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 ...
Berlin2023SMOOTH APPROXIMATIONS FOR FULLY NONLINEAR NONLOCAL ELLIPTIC EQUATIONS
We show that any viscosity solution to a general fully nonlinear nonlocal elliptic equation can be approximated by smooth (C infinity) solutions. ...
Providence2023On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem
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 PUBL2021Free Boundary Regularity for Almost Every Solution to the Signorini Problem
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 ...
2021Obesity-associated deficits in inhibitory control are phenocopied to mice through gut microbiota changes in one-carbon and aromatic amino acids metabolic pathways
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. Methods We studied gut microbiome composition and ...
BMJ PUBLISHING GROUP2021Iron 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 ...
BMC2021Obesity Impairs Short-Term and Working Memory through Gut Microbial Metabolism of Aromatic Amino Acids
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