We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
@article{ASNSP_2010_5_9_1_111_0,
author = {De Silva, Daniela and Valdinoci, Enrico},
title = {A fully nonlinear problem with free boundary in the plane},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {111--132},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {1},
year = {2010},
mrnumber = {2668875},
zbl = {1196.35232},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2010_5_9_1_111_0/}
}
TY - JOUR AU - De Silva, Daniela AU - Valdinoci, Enrico TI - A fully nonlinear problem with free boundary in the plane JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 111 EP - 132 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_1_111_0/ LA - en ID - ASNSP_2010_5_9_1_111_0 ER -
%0 Journal Article %A De Silva, Daniela %A Valdinoci, Enrico %T A fully nonlinear problem with free boundary in the plane %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 111-132 %V 9 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2010_5_9_1_111_0/ %G en %F ASNSP_2010_5_9_1_111_0
De Silva, Daniela; Valdinoci, Enrico. A fully nonlinear problem with free boundary in the plane. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 1, pp. 111-132. http://www.numdam.org/item/ASNSP_2010_5_9_1_111_0/
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