167 citations · 305 across the 38 of their papers we have counts for
47 papers
Minimizers for boundary reactions: renormalized energy, location of singularities, and applications
Xavier Cabre, Neus Consul, Matthias Kurzke
The Casten-Holland and Matano theorem for interior reactions states that no nonconstant stable solutions exist in convex domains of under zero Neumann boundary c…
Stable solutions to reaction-diffusion elliptic problems
Xavier Cabre
We are concerned with stable solutions to reaction-diffusion elliptic PDEs. We begin with regularity questions, first addressing the classical Laplacian. In joint work with Figalli…
Regularity of stable solutions to the MEMS problem up to the optimal dimension 6
Renzo Bruera, Xavier Cabre
In this article we address the regularity of stable solutions to semilinear elliptic equations with MEMS type nonlinearities. More precisely, we will have $0\leq u \le…
Estimates controlling a function by only its radial derivative and applications to stable solutions of elliptic equations
Xavier Cabre
We establish two new estimates which control a function (after subtracting its average) in by only the norm of its radial derivative. While the interior estimate holds…
Existence and symmetry of periodic nonlocal-CMC surfaces via variational methods
Xavier Cabre, Gyula Csató, Albert Mas
This paper provides the first variational proof of the existence of periodic nonlocal-CMC surfaces. These are nonlocal analogues of the classical Delaunay cylinders. More precisely…
Hölder regularity of stable solutions to semilinear elliptic equations up to : full quantitative proofs
Xavier Cabre
This article concerns the results obtained in [Cabré, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)], which established the Hölder regularity of stable solutions to semilinea…