Convergence of the solutions of the discounted Hamilton-Jacobi equation

• 成果类型: Article
• 署名作者: Davini, Andrea; Fathi, Albert; Iturriaga, Renato; Zavidovique, Maxime
• 署名单位: Sapienza University Rome; Ecole Normale Superieure de Lyon (ENS de LYON); CIMAT - Centro de Investigacion en Matematicas; Sorbonne Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0648-6
• 发表日期: 2016
• 页码: 29-55
• 关键词: point-of-view; VISCOSITY SOLUTIONS; lagrangian systems; weak kam

摘要

We consider a continuous coercive Hamiltonian H on the cotangent bundle of the compact connected manifold M which is convex in the momentum. If is the viscosity solution of the discounted equation where c(H) is the critical value, we prove that converges uniformly, as , to a specific solution of the critical equation We characterize in terms of Peierls barrier and projected Mather measures. As a corollary, we infer that the ergodic approximation, as introduced by Lions, Papanicolaou and Varadhan in 1987 in their seminal paper on homogenization of Hamilton-Jacobi equations, selects a specific corrector in the limit.