Calculus of Variations and Geometric Measure Theory

A. Figalli - D. Gomes - D. Marcon

Weak KAM Theory for a Weakly Coupled System of Hamilton-Jacobi Equations

created by figalli on 31 May 2016


Accepted Paper

Inserted: 31 may 2016
Last Updated: 31 may 2016

Journal: Calc. Var. Partial Differential Equations
Year: 2016


Here, we extend the weak KAM and Aubry-Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton-Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi's weak KAM theorem, and describe the asymptotic limit of the generalized Lax-Oleinik semigroup.