The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function
Author
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-12-25
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We define and study C 1 -solutions of the Aronsson equation (AE), a second order quasi linear equation.
We show that such super/subsolutions make the Hamiltonian monotone on the trajectories of the closed loop Hamiltonian dynamics.
We give a short, general proof that C 1 -solutions are absolutely minimizing functions.
We discuss how C 1 -supersolutions of (AE) become special Lyapunov functions of symmetric control systems, and allow to find continuous feedbacks driving the system to a target in finite time, except on a singular manifold.
A consequence is a simple proof that the corresponding minimum time function is locally Lipschitz continuous away from the singular manifold, despite classical results showing that it should only be Hölder continuous unless appropriate conditions hold.
We provide two examples for Hörmander and Grushin families of vector fields where we construct C 1 -solutions (even classical) explicitly.
American Psychological Association (APA)
Soravia, Pierpaolo. 2019. The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function. Abstract and Applied Analysis،Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1114490
Modern Language Association (MLA)
Soravia, Pierpaolo. The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function. Abstract and Applied Analysis No. 2019 (2019), pp.1-9.
https://search.emarefa.net/detail/BIM-1114490
American Medical Association (AMA)
Soravia, Pierpaolo. The Aronsson Equation, Lyapunov Functions, and Local Lipschitz Regularity of the Minimum Time Function. Abstract and Applied Analysis. 2019. Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1114490
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1114490