A Liouville theorem for solutions of the Monge-Ampère equation with periodic data
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 97-120. 
@article{AIHPC_2004__21_1_97_0,
     author = {Caffarelli, L and Li, Yan Yan},
     title = {A {Liouville} theorem for solutions of the {Monge-Amp\`ere} equation with periodic data},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {97--120},
     publisher = {Elsevier},
     volume = {21},
     number = {1},
     year = {2004},
     doi = {10.1016/j.anihpc.2003.01.005},
     zbl = {1108.35051},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.01.005/}
}
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Caffarelli, L; Li, Yan Yan. A Liouville theorem for solutions of the Monge-Ampère equation with periodic data. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 97-120. doi : 10.1016/j.anihpc.2003.01.005. http://www.numdam.org/articles/10.1016/j.anihpc.2003.01.005/

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