论文标题
海森伯格组中非线性分数方程的障碍问题和perron方法
The obstacle problem and the Perron Method for nonlinear fractional equations in the Heisenberg group
论文作者
论文摘要
我们研究了与广泛的非线性全差异算子相关的障碍问题，其模型是海森伯格组的分数sublaplacian。我们证明了解决方案的存在和唯一性，并且解决方案继承了障碍物的规律性特性，例如边界，连续性和hölder连续性，直到边界。我们还证明了对我们正在处理的问题类别的薄弱的超溶液的一些独立属性。在上述结果中，我们最终通过证明其存在非常一般的边界数据来研究了Perron-Wiener-brelot广义解决方案。
We study the obstacle problem related to a wide class of nonlinear integro-differential operators, whose model is the fractional subLaplacian in the Heisenberg group. We prove both the existence and uniqueness of the solution, and that solutions inherit regularity properties of the obstacle such as boundedness, continuity and Hölder continuity up to the boundary. We also prove some independent properties of weak supersolutions to the class of problems we are dealing with. Armed with the aforementioned results, we finally investigate the Perron-Wiener-Brelot generalized solution by proving its existence for very general boundary data.
