Geodesic
On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, pp. 181-197

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In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in ℝ 2 . We prove that if the level lines of a solution have bounded curvature, then these level lines are straight lines. As a consequence, the solution is one-dimensional. The method also provides a result on free boundary problems of Serrin type.

Classification : 35J40, 35J30, 35J65, 35R35, 35J99 
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     title = {On a {Liouville} type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {181--197},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {1},
     year = {2003},
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     zbl = {1170.35380},
     language = {en},
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Dolbeault, Jean; Monneau, Régis. On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 1, pp. 181-197. http://geodesic.mathdoc.fr/item/ASNSP_2003_5_2_1_181_0/