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

We study nonlinear elliptic equations of the form $F\left({D}^{2}u\right)=f\left(u\right)$ where the main assumption on $F$ and $f$ is that there exists a one dimensional solution which solves the equation in all the directions $\xi \in {ℝ}^{n}$. 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
@article{ASNSP_2008_5_7_3_369_0,
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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 7},
number = {3},
year = {2008},
pages = {369-405},
zbl = {1181.35111},
mrnumber = {2466434},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2008_5_7_3_369_0}
}

Savin, Ovidiu. Entire solutions to a class of fully nonlinear elliptic equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 7 (2008) no. 3, pp. 369-405. http://www.numdam.org/item/ASNSP_2008_5_7_3_369_0/

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