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- Title
A convergence result for the ergodic problem for Hamilton–Jacobi equations with Neumann-type boundary conditions.
- Authors
Al-Aidarous, Eman S.; Alzahrani, Ebraheem O.; Ishii, Hitoshi; Younas, Arshad M. M.
- Abstract
We consider the ergodic (or additive eigenvalue) problem for the Neumann-type boundary-value problem for Hamilton–Jacobi equations and the corresponding discounted problems. Denoting by uλ the solution of the discounted problem with discount factor λ > 0, we establish the convergence of the whole family to a solution of the ergodic problem as λ → 0, and give a representation formula for the limit function via the Mather measures and Peierls function. As an interesting by-product, we introduce Mather measures associated with Hamilton–Jacobi equations with the Neumann-type boundary conditions. These results are variants of the main results in a recent paper by Davini et al., who study the same convergence problem on smooth compact manifolds without boundary.
- Publication
Proceedings of the Royal Society of Edinburgh: Section A: Mathematics, 2016, Vol 146, Issue 2, p225
- ISSN
0308-2105
- Publication type
Article
- DOI
10.1017/S0308210515000517