Lasry-Lions approximations for discounted Hamilton-Jacobi equations
Cui Chen, Wei Cheng, Qi Zhang
TL;DR
This paper investigates the Lasry-Lions approximation method applied to discounted Hamilton-Jacobi equations, utilizing kernels from fundamental solutions of time-dependent Tonelli Lagrangians, and explores its effects on viscosity solutions.
Contribution
It introduces a novel application of Lasry-Lions approximation to discounted Hamilton-Jacobi equations using time-dependent Tonelli Lagrangian kernels.
Findings
Effective approximation of viscosity solutions achieved
Enhanced understanding of Hamilton-Jacobi equations dynamics
Potential for improved numerical methods
Abstract
We study the Lasry-Lions approximation using the kernel determined by the fundamental solution with respect to a time-dependent Tonelli Lagrangian. This approximation process is also applied to the viscosity solutions of the discounted Hamilton-Jacobi equations.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Quantum chaos and dynamical systems · Stochastic processes and financial applications