167 citations · 305 across the 38 of their papers we have counts for
5 papers · 1 filter
Universal Hardy-Sobolev inequalities on hypersurfaces of Euclidean space
Xavier Cabre, Pietro Miraglio
In this paper we study Hardy-Sobolev inequalities on hypersurfaces of , all of them involving a mean curvature term and having universal constants independent of…
The optimal exponent in the embedding into the Lebesgue spaces for functions with gradient in the Morrey space
Xavier Cabre, Fernando Charro
We study the following natural question that, apparently, has not been well addressed in the literature: Given functions with support in the unit ball …
Stable solutions to semilinear elliptic equations are smooth up to dimension 9
Xavier Cabre, Alessio Figalli, Xavier Ros-Oton +1
In this paper we prove the following long-standing conjecture: stable solutions to semilinear elliptic equations are bounded (and thus smooth) in dimension . This result,…
A new proof of the boundedness results for stable solutions to semilinear elliptic equations
Xavier Cabre
We consider the class of stable solutions to semilinear equations in a bounded smooth domain of . Since 2010 an interior a priori bound for stab…
Calibrations and null-Lagrangians for nonlocal perimeters and an application to the viscosity theory
Xavier Cabre
For nonnegative even kernels , we consider the -nonlocal perimeter functional acting on sets. Assuming the existence of a foliation of space made of solutions of the associat…