Alberto Farina, Enrico Valdinoci
Rigidity results for elliptic PDEs 
with uniform limits: an abstract 
framework with applications
(236K, pdf)

ABSTRACT.  We provide an abstract framework for a symmetry result arising in a conjecture of G. W. Gibbons and we apply it to the fractional Laplace operator, to the elliptic operators with constant 
coefficients, to the quasilinear operators 
and to the possibly nonuniformly elliptic fully nonlinear operators 
with possible gradient dependence.