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Article Dans Une Revue Inventiones Mathematicae Année : 2016

Convergence of the solutions of the discounted Hamilton–Jacobi equation

Résumé

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.
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hal-04502592 , version 1 (13-03-2024)

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Andrea Davini, Albert Fathi, Renato Iturriaga, Maxime Zavidovique. Convergence of the solutions of the discounted Hamilton–Jacobi equation. Inventiones Mathematicae, 2016, pp.29-55. ⟨10.1007/s00222-016-0648-6⟩. ⟨hal-04502592⟩
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