Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898795 | Journal of Differential Equations | 2018 | 12 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Pablo Mira,