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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.00628 |
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| _version_ | 1866910627044261888 |
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| author | Issa, Victor |
| author_facet | Issa, Victor |
| contents | We show that if a Hamilton-Jacobi equation admits a differentiable solution whose gradient is Lipschitz, then this solution is the unique semi-concave weak solution. Our result does not rely on any convexity (nor concavity) assumptions on the initial condition or the nonlinearity, and can therefore be utilized in contexts where the viscosity solution admits no standard variational representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak-Strong Uniqueness Principle for Hamilton-Jacobi Equations Issa, Victor Analysis of PDEs 35F21, 35D30, 35D40 We show that if a Hamilton-Jacobi equation admits a differentiable solution whose gradient is Lipschitz, then this solution is the unique semi-concave weak solution. Our result does not rely on any convexity (nor concavity) assumptions on the initial condition or the nonlinearity, and can therefore be utilized in contexts where the viscosity solution admits no standard variational representation. |
| title | Weak-Strong Uniqueness Principle for Hamilton-Jacobi Equations |
| topic | Analysis of PDEs 35F21, 35D30, 35D40 |
| url | https://arxiv.org/abs/2410.00628 |