Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929244055011328 |
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| author | Issa, Victor |
| author_facet | Issa, Victor |
| contents | It is well known that when the nonlinearity is convex, the Hamilton-Jacobi PDE admits a unique semi-convex weak solution, which is the viscosity solution. In this paper, motivated by problems arising from spin glasses, we show that if the Hamilton-Jacobi PDE with strictly convex nonlinearity and regular enough initial condition admits a semi-concave weak solution, then this solution is the viscosity solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations Issa, Victor Analysis of PDEs It is well known that when the nonlinearity is convex, the Hamilton-Jacobi PDE admits a unique semi-convex weak solution, which is the viscosity solution. In this paper, motivated by problems arising from spin glasses, we show that if the Hamilton-Jacobi PDE with strictly convex nonlinearity and regular enough initial condition admits a semi-concave weak solution, then this solution is the viscosity solution. |
| title | Uniqueness of semi-concave weak solutions for Hamilton-Jacobi equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.07665 |