Rigidity results for elliptic PDEs with uniform limits: an abstract framework with applications Alberto FarinaEnrico Valdinoci 35S0535J6035J61elliptic PDEsfractional or nonlinear operatorssymmetry results 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 elliptic fully nonlinear operators with possible gradient dependence. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4433 10.1512/iumj.2011.60.4433 en Indiana Univ. Math. J. 60 (2011) 121 - 142 state-of-the-art mathematics http://iumj.org/access/