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, Serie 5, Volume 2 (2003) no. 1, p. 181-197

In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in 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
@article{ASNSP_2003_5_2_1_181_0,
     author = {Dolbeault, Jean and Monneau, R\'egis},
     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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {1},
     year = {2003},
     pages = {181-197},
     zbl = {1170.35380},
     mrnumber = {1990978},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_181_0}
}
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, Serie 5, Volume 2 (2003) no. 1, pp. 181-197. http://www.numdam.org/item/ASNSP_2003_5_2_1_181_0/

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