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Entire solutions to a class of fully nonlinear elliptic equations

Ovidiu Savin — 2008

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study nonlinear elliptic equations of the form F ( D 2 u ) = f ( u ) where the main assumption on F and f is that there exists a one dimensional solution which solves the equation in all the directions ξ n . We show that entire monotone solutions u are one dimensional if their 0 level set is assumed to be Lipschitz, flat or bounded from one side by a hyperplane.

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