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arXiv · 1606.05486

On Lipschitz vector fields and the Cauchy problem in homogeneous groups

Valentino Magnani·Dario Trevisan
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Abstract

We introduce a class of "Lipschitz horizontal" vector fields in homogeneous groups, for which we show equivalent descriptions, e.g. in terms of suitable derivations. We then investigate the associated Cauchy problem, providing a uniqueness result both at equilibrium points and for vector fields of an involutive submodule of Lipschitz horizontal vector fields. We finally exhibit a counterexample to the general well-posedness theory for Lipschitz horizontal vector fields, in contrast with the Euclidean theory.

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Valentino Magnani, Dario Trevisan. 2016-06-17. On Lipschitz vector fields and the Cauchy problem in homogeneous groups. https://doi.org/10.1142/s0219199717500572

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