33 citations · 33 across the 14 of their papers we have counts for
17 papers
The stability conjecture for the Bernoulli problem in dimension four
Xavier Fernández-Real, Joaquim Serra
We prove that every global classical stable solution to the one-phase Bernoulli problem in is one-dimensional. In particular, if nonempty, its free boundary consists…
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…
The fractional Laplacian in Lipschitz domains: Dahlberg's Theorem and -solvability
Roberto Colombo, Xavier Fernández-Real, Xavier Ros-Oton
Given and a bounded Lipschitz domain , we establish a quantitative Dahlberg theory for the -harmonic measure of , . In the nonloc…
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…
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 th…
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…