4 citations · 11 across the 6 of their papers we have counts for
6 papers
A fully nonlinear problem with free boundary in the plane
Daniela De Silva, Enrico Valdinoci
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and co…
Stable solutions of elliptic equations on Riemannian manifolds
Alberto Farina, Yannick Sire, Enrico Valdinoci
This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. A…
Fibered nonlinearities for -Laplace equations
Milena Chermisi, Enrico Valdinoci
In , endowed with coordinates , we consider the PDE $$ -{\rm div} \big(α(\x) |\nabla u(\X)|^{p(x)-2}\nabla u(\X)\big)=f(x,u(\X)).$$ We prove a geometri…
On the Allen-Cahn equation in the Grushin plane: a monotone entire solution that is not one-dimensional
Isabeau Birindelli, Enrico Valdinoci
We consider solutions of the Allen-Cahn equation in the whole Grushin plane and we show that if they are monotone in the vertical direction, then they are stable and they satisfy a…
Rigidity results for some boundary quasilinear phase transitions
Yannick Sire, Enrico Valdinoci
We consider a quasilinear equation given in the half-space, i.e. a so called boundary reaction problem. Our concerns are a geometric Poincaré inequality and, as a byproduct of this…
Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
Yannick Sire, Enrico Valdinoci
We deal with symmetry properties for solutions of nonlocal equations of the type $(-Δ)^s v= f(v)\qquad {in $\R^n$,}$ where and the operator is the so-called…