Inserted: 29 apr 2010
Journal: Trans. of the AMS
Several new 1-D results for solutions of possibly singular or degenerate elliptic equations, inspired by a conjecture of De Giorgi, are provided. In particular, 1-D symmetry is proven under the assumption that either the profiles at infinity are 2-D, or that one level set is a complete graph, or that the solution is minimal or, more generally, Q-minimal.