Calculus of Variations and Geometric Measure Theory

V. Magnani - D. Trevisan

On Lipschitz vector fields and the Cauchy problem in homogeneous groups

created by magnani on 17 Jun 2016
modified by trevisan on 05 Jul 2024


Published Paper

Inserted: 17 jun 2016
Last Updated: 5 jul 2024

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

ArXiv: 1606.05486 PDF
Links: online version


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.