Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations

Alessio Figalli; Diogo Gomes; Diego Marcon

doi:10.1007/s00526-016-1016-5

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Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations

Journal article

Peer reviewed

Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations

Alessio Figalli, Diogo Gomes and Diego Marcon

Calculus of variations and partial differential equations, Vol.55(4), pp.1-32

01/08/2016

DOI: https://doi.org/10.1007/s00526-016-1016-5

Abstract

Mathematics

Mathematics, Applied

Physical Sciences

Science & Technology

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.

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Title: Weak KAM theory for a weakly coupled system of Hamilton-Jacobi equations
Creators - without role: Alessio Figalli - The University of Texas at Austin
Diogo Gomes - King Abdullah University of Science and Technology
Diego Marcon - Universidade Federal do Rio Grande do Sul
Publication Details: Calculus of variations and partial differential equations, Vol.55(4), pp.1-32
Publisher: Springer Nature
Number of pages: 32
Grant note: SFRH/BD/33919/2009 / UT Austin-Portugal partnership through the FCT doctoral fellowship DMS-1262411; DMS-1361122 / NSF; National Science Foundation (NSF) KAUST baseline and start-up funds
Identifiers: 9944069908331
Academic Unit: King Abdullah University of Science & Technology
Language: English
Resource Type: Journal article