Overdetermined elliptic problems in topological disks |
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Authors: | Pablo Mira |
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Institution: | Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain |
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Abstract: | We introduce a method, based on the Poincaré–Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems. |
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Keywords: | 35J25 53A10 |
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