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arXiv · 2205.10503

A Rademacher type theorem for Hamiltonians $H(x,p)$ and application to absolute minimizers

Jiayin Liu·Yuan Zhou
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Abstract

We establish a Rademacher type theorem involving Hamiltonians $H(x,p)$ under very weak conditions in both of Euclidean and Carnot-Carath\'eodory spaces. In particular,$H(x,p)$ is assumed to be only measurable in the variable $x$, and to be quasiconvex and lower-semicontinuous in the variable $p$. Without the lower-semicontinuity in the variable $p$, we provide a counter example showing the failure of such a Rademacher type theorem. Moreover, by applying such a Rademacher type theorem we build up an existence result of absolute minimizers for the corresponding $L^\infty$-functional. These improve or extend several known results in the literature.

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BibTeXRIS

Jiayin Liu, Yuan Zhou. 2022-05-21. A Rademacher type theorem for Hamiltonians $H(x,p)$ and application to absolute minimizers. https://arxiv.org/abs/2205.10503

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