08-28 Alberto Farina, Enrico Valdinoci

1D symmetry for solutions of semilinear and quasilinear elliptic equations (351K, pdf) Feb 12, 08

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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.

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