The regularity with respect to domains of the additive eigenvalues of superquadratic Hamilton--Jacobi equation
| Autor: | Bozorgnia, Farid, Kwon, Dohyun, Tu, Son N. T. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Differential Equations 402 (2024), 518-553 |
| Druh dokumentu: | Working Paper |
| Popis: | We study the additive eigenvalues on changing domains, along with the associated vanishing discount problems. We consider the convergence of the vanishing discount problem on changing domains for a general scaling type $\Omega_\lambda = (1+r(\lambda))\Omega$ with a continuous function $r$ and a positive constant $\lambda$. We characterize all solutions to the ergodic problem on $\Omega$ in terms of $r$. In addition, we demonstrate that the additive eigenvalue $\lambda\mapsto c_{\Omega_\lambda}$ on a rescaled domain $\Omega_\lambda = (1+\lambda)\Omega$ possesses one-sided derivatives everywhere. Additionally, the limiting solution can be parameterized by a real function, and we establish a connection between the regularity of this real function and the regularity of $\lambda \mapsto c_{\Omega_\lambda}$. We provide examples where higher regularity is achieved. Comment: 28 pages, typos corrected, final version |
| Databáze: | arXiv |
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