Alberto Farina, Enrico Valdinoci
1D symmetry for solutions 
of semilinear and quasilinear 
elliptic equations
(351K, pdf)

ABSTRACT.  Several new 1D results for solutions of possibly singular or degenerate 
elliptic equations, inspired by a conjecture of De Giorgi, are provided. 
In particular, 1D symmetry is proven under the assumption that either the profiles at infinity are 2D, or that one level set is a complete graph, or that the solution is minimal or, more 
generally, Q-minimal.