7 citations · 15 across the 8 of their papers we have counts for
20 papers · 1 filter
Global Schauder theory for minimizers of the energy
Mouhamed Moustapha Fall, Xavier Ros-Oton
We study the regularity of minimizers of the functional . This corresponds to understanding solutions for the regional fractional Laplacia…
The singular set in the Stefan problem
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
In this paper we analyze the singular set in the Stefan problem and prove the following results: - The singular set has parabolic Hausdorff dimension at most . - The solution…
Non-symmetric stable operators: regularity theory and integration by parts
Serena Dipierro, Xavier Ros-Oton, Joaquim Serra +1
We study solutions to in , being the generator of any, possibly non-symmetric, stable Lévy process. On the one hand, we study the regularity of solu…
The Neumann problem for the fractional Laplacian: regularity up to the boundary
Alessandro Audrito, Juan-Carlos Felipe-Navarro, Xavier Ros-Oton
We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if is a weak solution of in , $\mathc…
Sharp quantitative stability for isoperimetric inequalities with homogeneous weights
Eleonora Cinti, Federico Glaudo, Aldo Pratelli +2
We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homog…
Free boundary regularity for almost every solution to the Signorini problem
Xavier Fernández-Real, Xavier Ros-Oton
We investigate the regularity of the free boundary for the Signorini problem in . It is known that regular points are -dimensional and . However,…