Overdetermined elliptic problems in topological disks
Analysis of PDEs
2016-10-28 v1 Differential Geometry
Abstract
We introduce a method, based on the Poincare-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.
Cite
@article{arxiv.1610.08892,
title = {Overdetermined elliptic problems in topological disks},
author = {Pablo Mira},
journal= {arXiv preprint arXiv:1610.08892},
year = {2016}
}
Comments
10 pages