Overdetermined elliptic problems in simply connected planar domains
Proceedings:
Seminario de geometría ICMAT
Year of publication: 2018
Type: Conference paper
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 analogueof Hopf’s uniqueness theorem for constant mean curvature spheres, but for the general analytic context ofoverdetermined elliptic problems.