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.

1D symmetry for solutions of semilinear and quasilinear elliptic equations / A. Farina, E. Valdinoci. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 363:2(2011), pp. 579-609.

1D symmetry for solutions of semilinear and quasilinear elliptic equations

E. Valdinoci
2011

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.
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/223883
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