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arXiv · 1710.10887

On geodesics in low regularity

Clemens Sämann·Roland Steinbauer
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Abstract

We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle interrelation with solutions of the geodesic equations. Then we turn to the initial value problem for geodesics for locally Lipschitz continuous metrics and generalize recent results on existence, regularity and uniqueness of solutions in the sense of Filippov.

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Clemens Sämann, Roland Steinbauer. 2018-01-15. On geodesics in low regularity. https://doi.org/10.1088/1742-6596%2F968%2F1%2F012010

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