标题： 非凸Hamilton-Jacobi方程的梯度约束 显示英文标题

标题： Non-convex Hamilton-Jacobi equations with gradient constraints

摘要： 我们研究在梯度约束存在的情况下非凸的Hamilton-Jacobi方程，并为解产生了新的、最优的正则性结果。 这些方程的一个显著特点是梯度范数存在下界；它与控制问题的椭圆算子竞争，影响解的正则性。 这类模型与各种重要问题相关，并在多个领域有应用；特别感兴趣的是在风险理论中对多个保险公司最优分红问题的建模以及在可逆投资模型中的奇异随机控制。 显示英文摘要

摘要： 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.