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Mather theory for piecewise smooth Lagrangian systems

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Abstract

We establish the Mather theory for a type of piecewise smooth and positive definite Lagrangian systems. It models a mechanical system subject to external impulsive forcing. We show the existence of the minimal measure and the Lipschitz property of Aubry set. In addition, the weak KAM solution to this kind of piecewise smooth Lagrangian is also established.

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Authors and Affiliations

  1. School of Information Management, Nanjing University, Nanjing, 210093, China

    Min Zhou

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  1. Min Zhou
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Correspondence to Min Zhou.

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Zhou, M. Mather theory for piecewise smooth Lagrangian systems. Sci. China Math. 57, 1033–1044 (2014). https://doi.org/10.1007/s11425-013-4744-4

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  • DOI: https://doi.org/10.1007/s11425-013-4744-4

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