Non-convex Hamilton-Jacobi equations with gradient constraints
Analysis of PDEs
2020-10-27 v1
Abstract
We study non-convex Hamilton-Jacobi equations in the presence of gradient constraints and produce new, optimal, regularity results for the solutions. A distinctive feature of those equations regards the existence of a lower bound to the norm of the gradient; it competes with the elliptic operator governing the problem, affecting the regularity of the solutions. This class of models relates to various important questions and finds applications in several areas; of particular interest is the modeling of optimal dividends problems for multiple insurance companies in risk theory and singular stochastic control in reversible investment models.
Cite
@article{arxiv.2010.13622,
title = {Non-convex Hamilton-Jacobi equations with gradient constraints},
author = {Héctor A. Chang-Lara and Edgard A. Pimentel},
journal= {arXiv preprint arXiv:2010.13622},
year = {2020}
}