A Rigidity Result for Overdetermined Elliptic Problems in the Plane |
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| Authors: | Antonio Ros David Ruiz Pieralberto Sicbaldi |
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| Institution: | 1. Departamento de Geometría y Topología, Universidad de Granada Campus Fuentenueva, Granada, Spain;2. Departamento de Análisis Matemático, Universidad de Granada Campus Fuentenueva, Granada, Spain;3. Aix Marseille Université CNRS, Centrale Marseille I2M, UMR 7373, Marseille, France |
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| Abstract: | Let  be a (locally) Lipschitz function and  a  domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined elliptic problem ![]() we prove that Ω is a half‐plane. In particular, we obtain a partial answer to a question raised by H. Berestycki, L. Caffarelli, and L. Nirenberg in 1997.© 2017 Wiley Periodicals, Inc. |
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be a (locally) Lipschitz function and 
a 
domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined elliptic problem