Rate of convergence of the vanishing viscosity method for Hamilton–Jacobi equations with Neumann boundary conditions
Abstract
In this paper, we study the quantitative small noise limit in the [Formula: see text] norm of certain time-dependent Hamilton–Jacobi equations equipped with Neumann boundary conditions, depending on the regularity of the data and the geometric properties of the domain. We first provide a [Formula: see text] rate of convergence for Hamilton–Jacobi equations with locally Lipschitz Hamiltonians posed on convex domains of the Euclidean space. We then enhance this speed of convergence in the case of quadratic Hamiltonians proving one-side rates of order [Formula: see text] and [Formula: see text], [Formula: see text]. The results exploit recent [Formula: see text] contraction estimates for Fokker–Planck equations with bounded velocity fields on unbounded domains used to derive differential Harnack estimates for the corresponding Neumann heat flow.
Fields of Study & Subjects
Stochastic processes and financial applications
Numerical methods in inverse problems
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Journal of Hyperbolic Differential Equations
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 23
- Issue
- 02
- Pages
- 241–255
- Publication date
- 1 June 2026
- Language
- EN