On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount

Zibo Wang, Jianlu Zhang

In this paper, we establish the convergence of solutions to the viscous Hamilton-Jacobi equation (with a Tonelli Hamiltonian): \[ λu +H(x, du)=\varepsilon(λ)Δu,\quad λ>0 \] as $λ\r…