Calculus of Variations and Geometric Measure Theory
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A. Farina - E. Valdinoci

1-D symmetry for solutions of semilinear and quasilinear elliptic equations

created by farina on 29 Apr 2010


Accepted Paper

Inserted: 29 apr 2010

Journal: Trans. of the AMS
Year: 2009


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.


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