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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 $fin mathrm{C}^2(overline{Omega})$ 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.
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates on the vi
We study state-constraint static Hamilton-Jacobi equations in a sequence of domains ${Omega_k}_{k in mathbb{N}}$ in $mathbb{R}^n$ such that $Omega_k subset Omega_{k+1}$ for all $kin mathbb{N}$. We obtain rates of convergence of $u_k$, the solution to
We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. Far from the origin, we assume that the considered hamiltonian is close
In quantitative genetics, viscosity solutions of Hamilton-Jacobi equations appear naturally in the asymptotic limit of selection-mutation models when the population variance vanishes. They have to be solved together with an unknown function I(t) that
The non-exponential Schilder-type theorem in Backhoff-Veraguas, Lacker and Tangpi [Ann. Appl. Probab., 30 (2020), pp. 1321-1367] is expressed as a convergence result for path-dependent partial differential equations with appropriate notions of genera