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Representation Formulas for Contact Type Hamilton-Jacobi Equations

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Abstract

We discuss various kinds of representation formulas for the viscosity solutions of the contact type Hamilton-Jacobi equations by using the Herglotz’ variational principle.

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Notes

  1. Let (X, d) be a metric space. A function \(\phi :X\rightarrow {\mathbb {R}}\) is called \((\kappa _1,\kappa _2)\)-Lipschitz in the large if there exist \(\kappa _1,\kappa _2\geqslant 0\) such that \(|\phi (y)-\phi (x)|\leqslant \kappa _1+\kappa _2d(x,y)\), for all \(x,y\in X\)

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Acknowledgements

Wei Cheng is partly supported by National Natural Science Foundation of China (Grant No. 11871267, 11631006 and 11790272). Shengqing Hu is partly supported by China Postdoctoral Science Foundation (No. 003056). The authors thank for Qinbo Chen for helpful discussion. The authors would like to thank the anonymous referees for their careful reading and useful comments on the original version of this paper, which have helped us to improve the presentation significantly.

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  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Jiahui Hong, Wei Cheng, Shengqing Hu & Kai Zhao

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  1. Jiahui Hong
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  2. Wei Cheng
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  4. Kai Zhao
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Correspondence to Wei Cheng.

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Hong, J., Cheng, W., Hu, S. et al. Representation Formulas for Contact Type Hamilton-Jacobi Equations. J Dyn Diff Equat 34, 2315–2327 (2022). https://doi.org/10.1007/s10884-021-09960-w

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