| 概要 |
The Hamilton-Jacobi equation in general metric spaces recently attracts a great deal of attention because of its broad applications in optimal transport, mean field theory, traffic flow, neural networks, etc. In this talk, we focus on the eikonal equation, a special case of the Hamilton-Jacobi equation. After giving a review of fundamental results in the Euclidean space, we compare several known notions of metric viscosity solutions and show the equivalence of these notions in a complete length space.
This talk is based on joint work with Nageswari Shanmugalingam (U. Cincinnati) and Xiaodan Zhou (OIST).
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