Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913588946403328 |
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| author | Camilli, Fabio Goffi, Alessandro Mendico, Cristian |
| author_facet | Camilli, Fabio Goffi, Alessandro Mendico, Cristian |
| contents | We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theorems. Our approach is based on duality techniques à la Evans and a careful study of advection-diffusion equations. The optimality of the results is discussed by several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12932 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method Camilli, Fabio Goffi, Alessandro Mendico, Cristian Analysis of PDEs We provide some new integral estimates for solutions to Hamilton-Jacobi equations and we discuss several consequences, ranging from $L^p$-rates of convergence for the vanishing viscosity approximation to regularizing effects for the Cauchy problem in the whole Euclidean space and Liouville-type theorems. Our approach is based on duality techniques à la Evans and a careful study of advection-diffusion equations. The optimality of the results is discussed by several examples. |
| title | Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.12932 |