The vanishing discount problem for nonlocal Hamilton-Jacobi equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909581597212672 |
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| author | Davini, Andrea Ishii, Hitoshi |
| author_facet | Davini, Andrea Ishii, Hitoshi |
| contents | We establish a convergence result for the vanishing discount problem in the context of nonlocal HJ equations. We consider a fairly general class of discounted first-order and convex HJ equations which incorporate an integro-differential operator posed on the $d$-dimensional torus, and we show that the solutions converge to a specific critical solution as the discount factor tends to zero. Our approach relies on duality techniques for nonlocal convex HJ equations, building upon Hahn-Banach separation theorems to develop a generalized notion of Mather measure. The results are applied to a specific class of convex and superlinear Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The vanishing discount problem for nonlocal Hamilton-Jacobi equations Davini, Andrea Ishii, Hitoshi Analysis of PDEs Functional Analysis We establish a convergence result for the vanishing discount problem in the context of nonlocal HJ equations. We consider a fairly general class of discounted first-order and convex HJ equations which incorporate an integro-differential operator posed on the $d$-dimensional torus, and we show that the solutions converge to a specific critical solution as the discount factor tends to zero. Our approach relies on duality techniques for nonlocal convex HJ equations, building upon Hahn-Banach separation theorems to develop a generalized notion of Mather measure. The results are applied to a specific class of convex and superlinear Hamiltonians. |
| title | The vanishing discount problem for nonlocal Hamilton-Jacobi equations |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2504.11789 |