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3 results

7 - Lie Groups and Left-Invariant Sub-RiemannianStructures
Andrei Agrachev, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Davide Barilari, Université de Paris VII (Denis Diderot), Ugo Boscain, Centre National de la Recherche Scientifique (CNRS), Paris
Book:

A Comprehensive Introduction to Sub-Riemannian Geometry

Published online:

28 October 2019

Print publication:

31 October 2019, pp 191-245
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Summary

In this chapter we study normal Pontryagin extremals onleft-invariant sub-Riemannian structures on a Liegroup $G$. Such structures provide most of theexamples in which normal Pontryagin extremals can becomputed explicitly in terms of elementaryfunctions. We introduce Lie groups by studyingsubgroups of the group of diffeomorphisms of amanifold $M$ induced by a family of vector fieldswhose Lie algebra is finite dimensional.

An application of the theorem on Sums to viscosity solutions of degenerate fully nonlinear equations
Part of
Fausto Ferrari
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 2 / April 2020

Published online by Cambridge University Press:

26 January 2019, pp. 975-992

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April 2020
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We prove Hölder continuous regularity of bounded, uniformly continuous, viscosity solutions of degenerate fully nonlinear equations defined in all of ℝn space. In particular, the result applies also to some operators in Carnot groups.

Homogenization of Hamilton-Jacobi equations in Carnot Groups
Bianca Stroffolini
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 13 / Issue 1 / January 2007

Published online by Cambridge University Press:

14 February 2007, pp. 107-119

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January 2007
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We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups. The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property.

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3 results

7 - Lie Groups and Left-Invariant Sub-RiemannianStructures

Summary

An application of the theorem on Sums to viscosity solutions of degenerate fully nonlinear equations

Homogenization of Hamilton-Jacobi equations in Carnot Groups