2 citations · 3 across the 4 of their papers we have counts for
4 papers
Gradient estimates for the Green kernel under spectral Ricci bounds, and the stable Bernstein theorem in
Xavier Cabre, Giovanni Catino, Luciano Mari +2
We describe a method to prove new integral inequalities for stable minimal hypersurfaces in Euclidean space. As an application, we give a simple proof that complete, two sided, sta…
Periodic solutions to integro-differential equations: variational formulation, symmetry, and regularity
Xavier Cabre, Gyula Csató, Albert Mas
We consider nonconstant periodic constrained minimizers of semilinear elliptic equations for integro-differential operators in . We prove that, after an appropriate tra…
Null-Lagrangians and calibrations for general nonlocal functionals and an application to the viscosity theory
Xavier Cabre, Iñigo U. Erneta, Juan-Carlos Felipe-Navarro
In this article we build a null-Lagrangian and a calibration for general nonlocal elliptic functionals in the presence of a field of extremals. Thus, our construction assumes the e…
A Weierstrass extremal field theory for the fractional Laplacian
Xavier Cabre, Iñigo U. Erneta, Juan-Carlos Felipe-Navarro
In this paper we extend, for the first time, part of the Weierstrass extremal field theory in the Calculus of Variations to a nonlocal framework. Our model case is the energy funct…