论文标题
弱椭圆形汉密尔顿 - 雅各比 - 贝尔曼方程的周期性均质化，具有关键的分数扩散
Periodic Homogenization for Weakly Elliptic Hamilton-Jacobi-Bellman Equations with Critical Fractional Diffusion
论文作者
论文摘要
在本文中，我们建立了汉密尔顿 - 雅各比 - 贝尔曼（HJB）方程的周期性均质化，该方程与非局部差异类型的非局部操作员相关。当分数扩散与漂移项相同并且椭圆形较弱时，我们会考虑这种情况。本文的结果是双重的。一只手，我们为弱椭圆形非本地HJB提供Lipschitz的规律性结果，从而扩展了先前在[8]中获得的结果。另一方面，我们基于一半放松的限制和有效问题的比较原则建立了收敛结果。后者强烈依赖于有效的哈密顿量的规律性和椭圆形性能，为此，纠正器的精细lipschitz起着至关重要的作用。
In this paper we establish periodic homogenization for Hamilton-Jacobi-Bellman (HJB) equations, associated to nonlocal operators of integro-differential type. We consider the case when the fractional diffusion has the same order as the drift term, and is weakly elliptic. The outcome of the paper is twofold. One one hand, we provide Lipschitz regularity results for weakly elliptic non-local HJB, extending the results previously obtained in [8]. On the other hand, we establish a convergence result, based on half relaxed limits and a comparison principle for the effective problem. The latter strongly relies on the regularity and the ellipticity properties of the effective Hamiltonian, for which a fine Lipschitz estimate of the corrector plays a crucial role.
