Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces

TL;DR

This paper establishes convergence rates for singular perturbations of Hamilton-Jacobi equations in unbounded spaces, considering linear fast operators with Ornstein-Uhlenbeck drift and nonlinear slow operators, with results depending on source term regularity.

Contribution

It provides new convergence rate results for Hamilton-Jacobi equations with unbounded variables and Ornstein-Uhlenbeck type fast operators, under varying regularity conditions.

Findings

Derived multiple convergence rates based on source term regularity.

Extended analysis to unbounded spaces with Ornstein-Uhlenbeck drift.

Handled fully nonlinear elliptic slow operators.

Abstract

We prove rate of convergence results for singular perturbations of Hamilton-Jacobi equations in unbounded spaces where the fast operator is linear, uniformly elliptic and has an Ornstein-Uhlenbeck-type drift. The slow operator is a fully nonlinear elliptic operator while the source term is assumed only locally H\"older continuous in both fast and slow variables. We obtain several rates of convergence according on the regularity of the source term.