Global solutions to the eikonal equation

Details Global solutions to the eikonal equation Global solutions to the eikonal equation

2011-02-03

arxiv.org/abs/1102.0649v1

Physics

Mathematical Physics

35 pages

Scientific paper

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 Schr\"odinger operator theory.

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