Global solutions to the eikonal equation

[摘要] We study structural stability of smoothness of the maximal solution to the geometric eikonal equation on (R-d, G), d >= 2. This is within the framework of order zero metrics G. For a subclass of these metrics we show existence, stability as well as precise asymptotics for derivatives of the solution. These results are applicable to examples arising in Schrodinger operator theory. (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Geometric eikonal equation;Maximal solution;Order zero metrics;Structural stability