Xavier Fernandez-Real Girona | EPFL Graph Search

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

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

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