HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Convergence of the solutions of the discounted Hamilton–Jacobi equation

Abstract : We consider a continuous coercive Hamiltonian H on the cotangent bundle of the compact connected manifold M which is convex in the momentum. If uλ:M→ℝ is the viscosity solution of the discounted equation λuλ(x)+H(x,dxuλ)=c(H), where c(H) is the critical value, we prove that uλ converges uniformly, as λ→0, to a specific solution u0:M→ℝ of the critical equation H(x,dxu)=c(H). We characterize u0 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.
Document type :
Journal articles
Complete list of metadata

Contributor : Albert Fathi Connect in order to contact the contributor
Submitted on : Wednesday, December 7, 2016 - 6:53:48 PM
Last modification on : Tuesday, December 8, 2020 - 10:17:26 AM

Links full text




Albert Fathi. Convergence of the solutions of the discounted Hamilton–Jacobi equation. Inventiones Mathematicae, Springer Verlag, 2016, ⟨10.1007/s00222-016-0648-6⟩. ⟨ensl-01412048⟩



Record views