20 citations · 30 across the 4 of their papers we have counts for
4 papers
Regularity of minimizers of semilinear elliptic problems up to dimension four
Xavier Cabre
We consider the class of semi-stable solutions to semilinear equations in a bounded smooth domain of (with convex in some results). This class includes all…
Qualitative properties of saddle-shaped solutions to bistable diffusion equations
Xavier Cabre, Joana Terra
We consider the elliptic equation in the whole , where is of bistable type. It is known that there exists a saddle-shaped solution in . This is a…
Front propagation in Fisher-KPP equations with fractional diffusion
Xavier Cabre, Jean-Michel Roquejoffre
We study in this note the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with slowly decaying kernel, an important example being the fra…
Positive solutions of nonlinear problems involving the square root of the Laplacian
Xavier Cabre, Jinggang Tan
We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive so…