On the rate of convergence in superquadratic Hamilton--Jacobi equations with state constraints

2025/08/03 by Prerona Dutta, Dutta, Prerona, Khai T. Nguyen +3 · 3 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Optimization and Variational Analysis #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2508.01528

Abstract

In this paper, we investigate the convergence rate in the vanishing viscosity limit for solutions to superquadratic Hamilton--Jacobi equations with state constraints. For every p>2, we establish the rate of convergence for nonnegative Lipschitz data vanishing on the boundary to be of order O(ε^1/2) and obtain an improved upper rate of order O(ε^(p)/(2(p-1))) for semiconcave data.

Citations

• Convergence rates for the vanishing viscosity approximation of fully nonlinear, non-convex, second-order Hamilton-Jacobi equations
• Rate of convergence of the vanishing viscosity method for Hamilton-Jacobi equations with Neumann boundary conditions
• Convergence rates for the vanishing viscosity approximation of Hamilton-Jacobi equations: the convex case
• Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations
• Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications
• Policy iteration for the deterministic control problems -- a viscosity approach
• Global semiconcavity of solutions to first-order Hamilton-Jacobi equations with state constraints
• Remarks on the vanishing viscosity process of state-constraint Hamilton-Jacobi equations
• Viscosity solutions of general viscous Hamilton-Jacobi equations
• Large time behavior of solutions of viscous Hamilton-Jacobi Equations with superquadratic Hamiltonian
• Two approximations of solutions of Hamilton-Jacobi equations

Cited by

• Quantitative homogenization of Hamilton--Jacobi equations on perforated domains with Dirichlet boundary conditions
• State-Constrained Chemical Reactions: Discrete-to-Continuous Hamilton--Jacobi Equations and Large Deviations
• On the vanishing viscosity limit of Hamilton-Jacobi equations with nearly optimal discount

Related

• Remarks on the vanishing viscosity process of state-constraint Hamilton-Jacobi equations
• Convergence rates for the vanishing viscosity approximation of Hamilton-Jacobi equations: the convex case
• Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations
• Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations
• Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation