Published Paper

Inserted: 17 jun 2016
Last Updated: 25 dec 2020

Journal: Commun. Contemp. Math.
Volume: 20
Number: 5
Pages: 21
Year: 2018
Links: online version

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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