Smooth subsolutions of the discounted Hamilton-Jacobi equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909416110948352 |
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| author | Huang, Xiyao Jin, Liang Zhang, Jianlu Zhao, Kai |
| author_facet | Huang, Xiyao Jin, Liang Zhang, Jianlu Zhao, Kai |
| contents | For the discounted Hamilton-Jacobi equation,$$λu+H(x,d_x u)=0, \ x \in M, $$we construct $C^{1,1}$ subsolutions which are indeed solutions on the projected Aubry set. The smoothness of such subsolutions can be improved under additional hyperbolicity assumptions. As applications, we can use such subsolutions to identify the maximal global attractor of the associated conformally symplectic flow and to control the convergent speed of the Lax-Oleinik semigroups |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_10687 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Smooth subsolutions of the discounted Hamilton-Jacobi equations Huang, Xiyao Jin, Liang Zhang, Jianlu Zhao, Kai Dynamical Systems Analysis of PDEs For the discounted Hamilton-Jacobi equation,$$λu+H(x,d_x u)=0, \ x \in M, $$we construct $C^{1,1}$ subsolutions which are indeed solutions on the projected Aubry set. The smoothness of such subsolutions can be improved under additional hyperbolicity assumptions. As applications, we can use such subsolutions to identify the maximal global attractor of the associated conformally symplectic flow and to control the convergent speed of the Lax-Oleinik semigroups |
| title | Smooth subsolutions of the discounted Hamilton-Jacobi equations |
| topic | Dynamical Systems Analysis of PDEs |
| url | https://arxiv.org/abs/2007.10687 |