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, p. 111-132
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.
Classification:  35J60,  35N25,  35B06
@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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {1},
     year = {2010},
     pages = {111-132},
     zbl = {1196.35232},
     mrnumber = {2668875},
     language = {en},
     url = {http://www.numdam.org/item/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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