On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918376801042432 |
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| author | Dutta, Prerona Nguyen, Khai T. Tu, Son N. T. |
| author_facet | Dutta, Prerona Nguyen, Khai T. Tu, Son N. T. |
| contents | In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every $p>2$, we establish the rate of convergence for nonnegative Lipschitz data vanishing on the boundary to be of order $ \mathcal{O}(\varepsilon^{1/2}) $ and obtain an improved upper rate of order $ \mathcal{O}\big(\varepsilon^{\frac{p}{2(p-1)}}\big)$ for semiconcave data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints Dutta, Prerona Nguyen, Khai T. Tu, Son N. T. Analysis of PDEs 35B40, 35D40, 49J20, 49L25, 70H20 In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every $p>2$, we establish the rate of convergence for nonnegative Lipschitz data vanishing on the boundary to be of order $ \mathcal{O}(\varepsilon^{1/2}) $ and obtain an improved upper rate of order $ \mathcal{O}\big(\varepsilon^{\frac{p}{2(p-1)}}\big)$ for semiconcave data. |
| title | On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints |
| topic | Analysis of PDEs 35B40, 35D40, 49J20, 49L25, 70H20 |
| url | https://arxiv.org/abs/2508.01528 |