A fully nonlinear problem with free boundary in the plane

2008/11/10 by Daniela De Silva, Enrico Valdinoci, De Silva, Daniela +1
Computer Science · Mathematics · #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #msc:35J60

paper · pdf · doi:10.48550/arxiv.0811.1476

arxiv created 2008/11/10 · openalex publication_date 2008/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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