A Lagrangian Approach to Weakly Coupled Hamilton-Jacobi Systems
Analysis of PDEs
2015-03-03 v1
Abstract
We study a class of weakly coupled Hamilton-Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing the Lagrangians obtained by duality from the Hamiltonians of the system. We use them to characterize, by means of a suitable estimate, all the subsolutions of the system, and to explicitly represent some subsolutions enjoying an additional maximality property. A crucial step for our analysis is to put the problem in a suitable random frame. Only some basic knowledge of measure theory is required, and the presentation is accessible to readers without background in probability.
Cite
@article{arxiv.1503.00521,
title = {A Lagrangian Approach to Weakly Coupled Hamilton-Jacobi Systems},
author = {H. Mitake and A. Siconolfi and H. V. Tran and N. Yamada},
journal= {arXiv preprint arXiv:1503.00521},
year = {2015}
}