In this paper we establish a Liouville type theorem for fully nonlinear elliptic equations related to a conjecture of De Giorgi in . 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.
@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}, pages = {181--197}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {1}, year = {2003}, mrnumber = {1990978}, zbl = {1170.35380}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_1_181_0/} }
TY - JOUR AU - Dolbeault, Jean AU - Monneau, Régis TI - On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 181 EP - 197 VL - 2 IS - 1 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_1_181_0/ LA - en ID - ASNSP_2003_5_2_1_181_0 ER -
%0 Journal Article %A Dolbeault, Jean %A Monneau, Régis %T On a Liouville type theorem for isotropic homogeneous fully nonlinear elliptic equations in dimension two %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 181-197 %V 2 %N 1 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2003_5_2_1_181_0/ %G en %F 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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