Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909708926844928 |
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| author | Tu, Son N. T. Zhang, Jianlu |
| author_facet | Tu, Son N. T. Zhang, Jianlu |
| contents | We study the asymptotic behavior of solutions to the fully nonlinear Hamilton-Jacobi equation $H(x, Du, λu) = 0$ in $\mathbb{R}^n$ as $λ\to 0^+$. Under the assumption that the Aubry set is localized, we employ a variational approach to derive limiting Mather-type measures and formulate a selection principle. Central to our analysis is a modified variational formula that bridges global and local state-constraint solutions, thereby extending localization techniques to the nonlinear framework. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_20472 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains Tu, Son N. T. Zhang, Jianlu Analysis of PDEs 35D40, 70H20, 35J60, 37J40, 49L25, 37K99 We study the asymptotic behavior of solutions to the fully nonlinear Hamilton-Jacobi equation $H(x, Du, λu) = 0$ in $\mathbb{R}^n$ as $λ\to 0^+$. Under the assumption that the Aubry set is localized, we employ a variational approach to derive limiting Mather-type measures and formulate a selection principle. Central to our analysis is a modified variational formula that bridges global and local state-constraint solutions, thereby extending localization techniques to the nonlinear framework. |
| title | Vanishing discount limits for first-order fully nonlinear Hamilton-Jacobi equations on noncompact domains |
| topic | Analysis of PDEs 35D40, 70H20, 35J60, 37J40, 49L25, 37K99 |
| url | https://arxiv.org/abs/2507.20472 |