We study nonlinear elliptic equations of the form where the main assumption on and is that there exists a one dimensional solution which solves the equation in all the directions . We show that entire monotone solutions are one dimensional if their level set is assumed to be Lipschitz, flat or bounded from one side by a hyperplane.
@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},
pages = {369--405},
year = {2008},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 7},
number = {3},
mrnumber = {2466434},
zbl = {1181.35111},
language = {en},
url = {https://www.numdam.org/item/ASNSP_2008_5_7_3_369_0/}
}
TY - JOUR AU - Savin, Ovidiu TI - Entire solutions to a class of fully nonlinear elliptic equations JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2008 SP - 369 EP - 405 VL - 7 IS - 3 PB - Scuola Normale Superiore, Pisa UR - https://www.numdam.org/item/ASNSP_2008_5_7_3_369_0/ LA - en ID - ASNSP_2008_5_7_3_369_0 ER -
%0 Journal Article %A Savin, Ovidiu %T Entire solutions to a class of fully nonlinear elliptic equations %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2008 %P 369-405 %V 7 %N 3 %I Scuola Normale Superiore, Pisa %U https://www.numdam.org/item/ASNSP_2008_5_7_3_369_0/ %G en %F 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, Série 5, Tome 7 (2008) no. 3, pp. 369-405. https://www.numdam.org/item/ASNSP_2008_5_7_3_369_0/
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