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- W4295288232 abstract "We investigate the convergence rate in the vanishing viscosity process of the solutions to the subquadratic state-constraint Hamilton-Jacobi equations. We give two different proofs of the fact that, for nonnegative Lipschitz data that vanish on the boundary, the rate of convergence is $mathcal{O}(sqrt{varepsilon})$ in the interior. Moreover, the one-sided rate can be improved to $mathcal{O}(varepsilon)$ for nonnegative compactly supported data and $mathcal{O}(varepsilon^{1/p})$ (where $1<p<2$ is the exponent of the gradient term) for nonnegative data $fin mathrm{C}^2(bar{Omega})$ such that $f = 0$ and $Df = 0$ on the boundary. Our approach relies on deep understanding of the blow-up behavior near the boundary and semiconcavity of the solutions." @default.
- W4295288232 created "2022-09-12" @default.
- W4295288232 creator A5022509637 @default.
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- W4295288232 date "2021-07-20" @default.
- W4295288232 modified "2023-10-18" @default.
- W4295288232 title "Remarks on the vanishing viscosity process of state-constraint Hamilton-Jacobi equations" @default.
- W4295288232 doi "https://doi.org/10.48550/arxiv.2107.09860" @default.
- W4295288232 hasPublicationYear "2021" @default.
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