Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

V. Magnani - D. Trevisan

On Lipschitz vector fields and the Cauchy problem in homogeneous groups

created by magnani on 17 Jun 2016
modified on 03 Jun 2018

[BibTeX]

Accepted Paper

Inserted: 17 jun 2016
Last Updated: 3 jun 2018

Journal: Commun. Contemp. Math.
Year: 2016

ArXiv: 1606.05486 PDF
Links: published online

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.


Download:

Credits | Cookie policy | HTML 5 | CSS 2.1