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Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes

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Abstract

We continue the study of viscosity solutions of Hamilton–Jacobi equations in metric spaces initiated in [37]. We present a more complete account of the theory of metric viscosity solutions based on local slopes. Several comparison and existence results are proved and the main techniques for such metric viscosity solutions are illustrated.

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Acknowledgments

The research of W. Gangbo was supported by NSF grant DMS-1160939. The authors would like to thank a referee for commenting that the theory of metric viscosity solutions can be extended to complete metric spaces which are length spaces. It influenced us to include Remark 2.10 in the final version of the manuscript.

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  1. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Wilfrid Gangbo & Andrzej Święch

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  1. Wilfrid Gangbo
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  2. Andrzej Święch
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Correspondence to Wilfrid Gangbo.

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Communicated by Y. Giga.

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Gangbo, W., Święch, A. Metric viscosity solutions of Hamilton–Jacobi equations depending on local slopes. Calc. Var. 54, 1183–1218 (2015). https://doi.org/10.1007/s00526-015-0822-5

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