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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2206.12537 |
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| _version_ | 1866913408126812160 |
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| author | Chen, Hong-Bin Xia, Jiaming |
| author_facet | Chen, Hong-Bin Xia, Jiaming |
| contents | We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the well-posedness of the equation in the viscosity sense and prove several properties of the solution: monotonicity, Lipschitzness, and representations by variational formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12537 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hamilton-Jacobi equations with monotone nonlinearities on convex cones Chen, Hong-Bin Xia, Jiaming Analysis of PDEs 35A01, 35A02, 35D40, 35F21 We study the Cauchy problem of a Hamilton-Jacobi equation with the spatial variable in a closed convex cone. A monotonicity assumption on the nonlinearity allows us to prescribe no condition on the boundary of the cone. We show the well-posedness of the equation in the viscosity sense and prove several properties of the solution: monotonicity, Lipschitzness, and representations by variational formulas. |
| title | Hamilton-Jacobi equations with monotone nonlinearities on convex cones |
| topic | Analysis of PDEs 35A01, 35A02, 35D40, 35F21 |
| url | https://arxiv.org/abs/2206.12537 |