论文标题
最大$ l^q $ - 抛物线汉密尔顿 - 雅各布方程和应用的含义野外游戏的应用
Maximal $L^q$-regularity for parabolic Hamilton-Jacobi equations and applications to Mean Field Games
论文作者
论文摘要
在本文中，我们研究了具有时间依赖的粘性汉密尔顿 - 雅各比方程的最大$ l^q $ regulactility，其右侧无界的右侧和超线性生长。我们的方法基于新的积分和Hölder估计，插值不平等以及线性方程的抛物线规则性之间的相互作用。这些估计是通过双重性方法获得的。这为P.-L.猜想的抛物线寄生虫提供了新的光。作者最近在固定框架中解决了汉密尔顿 - 雅各比方程的最大规律性的狮子。最后，提供了针对具有无限本地耦合的现场游戏系统的经典解决方案的应用程序。
In this paper we investigate maximal $L^q$-regularity for time-dependent viscous Hamilton-Jacobi equations with unbounded right-hand side and superlinear growth in the gradient. Our approach is based on the interplay between new integral and Hölder estimates, interpolation inequalities, and parabolic regularity for linear equations. These estimates are obtained via a duality method à la Evans. This sheds new light on a parabolic counterpart of a conjecture by P.-L. Lions on maximal regularity for Hamilton-Jacobi equations, recently addressed in the stationary framework by the authors. Finally, applications to the existence problem of classical solutions to Mean Field Games systems with unbounded local couplings are provided.
