论文标题
静止的完全非线性平均场游戏
Stationary fully nonlinear mean-field games
论文作者
论文摘要
在本文中，我们研究了与最小化问题相关的完全非线性均值游戏。变异设置由功能取决于其通过其Hessian矩阵的论点而驱动。我们在相当自然的条件下工作，并为Sobolev空间中的解决方案建立了改进的（尖锐）规律性。然后，我们证明了为变异问题和平均场游戏系统的解决方案的存在而存在的最小化器。我们还研究了一个一维示例，并揭示了有关明确解决方案的新信息。我们的发现可以推广到更大的运营商，从而提供有关更广泛示例的信息。
In this paper we examine fully nonlinear mean-field games associated with a minimization problem. The variational setting is driven by a functional depending on its argument through its Hessian matrix. We work under fairly natural conditions and establish improved (sharp) regularity for the solutions in Sobolev spaces. Then, we prove the existence of minimizers for the variational problem and the existence of solutions to the mean-field games system. We also investigate a unidimensional example and unveil new information on the explicit solutions. Our findings can be generalized to a larger class of operators, yielding information on a broader range of examples.
