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math.AP2008★ 3 cited
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…
math.AP2008
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…
math.AP2008★ 2 cited
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…