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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18404 |
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| _version_ | 1866914119794294784 |
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| author | Davini, Andrea Saona, Raimundo Ziliotto, Bruno |
| author_facet | Davini, Andrea Saona, Raimundo Ziliotto, Bruno |
| contents | We prove stochastic homogenization for a class of non-convex and non-coercive first-order Hamilton-Jacobi equations in a finite-range-dependence environment for Hamiltonians that can be expressed by a max-min formula. Exploiting the representation of solutions as value functions of differential games, we develop a game-theoretic approach to homogenization. We furthermore extend this result to a class of Lipschitz Hamiltonians that need not admit a global max-min representation. Our methods allow us to get a quantitative convergence rate for solutions with linear initial data toward the corresponding ones of the effective limit problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18404 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Homogenization of HJ Equations: a Differential Game Approach Davini, Andrea Saona, Raimundo Ziliotto, Bruno Analysis of PDEs 35B27, 35F21, 91A23, 60K37 We prove stochastic homogenization for a class of non-convex and non-coercive first-order Hamilton-Jacobi equations in a finite-range-dependence environment for Hamiltonians that can be expressed by a max-min formula. Exploiting the representation of solutions as value functions of differential games, we develop a game-theoretic approach to homogenization. We furthermore extend this result to a class of Lipschitz Hamiltonians that need not admit a global max-min representation. Our methods allow us to get a quantitative convergence rate for solutions with linear initial data toward the corresponding ones of the effective limit problem. |
| title | Stochastic Homogenization of HJ Equations: a Differential Game Approach |
| topic | Analysis of PDEs 35B27, 35F21, 91A23, 60K37 |
| url | https://arxiv.org/abs/2406.18404 |