论文标题
无限分数拉普拉斯驱动的进化
Evolution Driven by the Infinity Fractional Laplacian
论文作者
论文摘要
我们认为与Bjorland，Caffarelli和Figalli（2012）引入的无限分数Laplacian相关的进化问题是非tug tug tug战争游戏的无限发电机。我们首先构建了有限和均匀连续数据的初始值问题的一类粘度解决方案。一个重要的结果是，当将非线性算子在较高的维度上与一维分数拉普拉斯式的等效性应用于径向对称和单调函数时。得益于这一点，以及经典和粘度解决方案之间的比较定理，我们能够建立全球性的不平等现象，尤其是解释了解决方案的长期行为。
We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland, Caffarelli and Figalli (2012) as the infinitesimal generator of a non-Brownian tug-of-war game. We first construct a class of viscosity solutions of the initial-value problem for bounded and uniformly continuous data. An important result is the equivalence of the nonlinear operator in higher dimensions with the one-dimensional fractional Laplacian when it is applied to radially symmetric and monotone functions. Thanks to this and a comparison theorem between classical and viscosity solutions, we are able to establish a global Harnack inequality that, in particular, explains the long-time behavior of the solutions.
