Heisenberg群中的水平拟凸包络
Horizontally quasiconvex envelope in the Heisenberg group
摘要：
研究了Heisenberg群中给定连续函数的水平拟凸（简称h-拟凸）包络的偏微分方程方法.我们根据一阶非局部Hamilton-Jacobi方程的粘性子解给出了上半连续h-拟凸函数的特征。我们还通过迭代非局部算子构造了连续函数的相应包络。证明了非局部Hamilton-Jacobi方程Dirichlet边值问题的黏性解的存在性和唯一性。我们的方法的应用程序的h-凸包的海森堡群中的一个给定的集合进行了讨论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
