$1$D symmetry for solutions of semilinear and quasilinear elliptic equations
$1$D symmetry for solutions of semilinear and quasilinear elliptic equations
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 …