Geodesic
Entire solutions to a class of fully nonlinear elliptic equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 369-405

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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∈ℝ 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.

Classification : 35J70, 35B65 
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     author = {Savin, Ovidiu},
     title = {Entire solutions to a class of fully nonlinear elliptic equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {369--405},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 7},
     number = {3},
     year = {2008},
     mrnumber = {2466434},
     zbl = {1181.35111},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_3_369_0/}
}
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Savin, Ovidiu. Entire solutions to a class of fully nonlinear elliptic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 3, pp. 369-405. http://geodesic.mathdoc.fr/item/ASNSP_2008_5_7_3_369_0/