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.
A fully nonlinear problem with free boundary in the plane / D. De Silva, E. Valdinoci. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - 9:1(2010), pp. 111-132.
A fully nonlinear problem with free boundary in the plane
E. Valdinoci
2010
Abstract
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.
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