论文标题
汉密尔顿 - 雅各比方程有梯度约束
Non-convex Hamilton-Jacobi equations with gradient constraints
论文作者
论文摘要
我们在存在梯度约束的情况下研究非凸汉密尔顿 - 雅各比方程，并为溶液产生新的，最佳的规律性结果。这些方程式的独特特征认为，梯度规范的下限存在；它与管理问题的椭圆操作员竞争，影响解决方案的规律性。这类模型涉及各种重要问题，并在几个领域找到了应用。特别有趣的是，在可逆投资模型中，在风险理论和奇异随机控制中为多家保险公司的最佳股息问题建模。
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.
