Global solutions to the eikonal equation
arXiv:1102.0649
Abstract
We study structural stability of smoothness of the maximal solution to the geometric eikonal equation on (Rd, G), d \geq 2. This is within the framework of order zero metrics G. For a subclass we show existence, stability as well as precise asymptotics for derivatives of the solution. These results are applicable for examples from Schrödinger operator theory.
35 pages