论文标题
Heisenberg Group中的水平Quasiconvex信封
Horizontally quasiconvex envelope in the Heisenberg group
论文作者
论文摘要
本文涉及Heisenberg组中给定连续功能的水平质子vex（短Quasiconvex）的基于PDE的方法。我们为上半连续的H Quasiconvex函数提供了一个表征，该函数是粘度订阅的一阶非局部汉密尔顿 - 雅各比方程的表征。我们还通过迭代非局部运算符来构建连续函数的相应包络。我们论点中的一个重要一步是证明非本地汉密尔顿 - 雅各比方程的迪利奇边界问题的粘度解决方案的独特性和存在。还讨论了我们在海森堡组中给定集合的H-Convex船体的应用。
This paper is concerned with a PDE-based approach to the horizontally quasiconvex (h-quasiconvex for short) envelope of a given continuous function in the Heisenberg group. We provide a characterization for upper semicontinuous, h-quasiconvex functions in terms of the viscosity subsolution to a first-order nonlocal Hamilton-Jacobi equation. We also construct the corresponding envelope of a continuous function by iterating the nonlocal operator. One important step in our arguments is to prove the uniqueness and existence of viscosity solutions to the Dirichlet boundary problems for the nonlocal Hamilton-Jacobi equation. Applications of our approach to the h-convex hull of a given set in the Heisenberg group are discussed as well.
