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【期刊论文】The complex Monge–Amp`ere equation with infinite boundary value☆
杨孝平, Ni Xiang, Xiao-Ping Yang
Nonlinear Analysis 68 (2008) 1075-1081,-0001,():
-1年11月30日
In this article we consider the complex Monge-Amp`ere equation with infinite boundary value in bounded pseudoconvex domains. We prove the existence of strictly plurisubharmonic solution to the problem in convex domains under suitable growth conditions.We also obtain, for general pseudoconvex domains, some nonexistence results which show that these growth conditions are nearly optimal.
Complex Monge–Amp`, ere equation, Infinite boundary value, Plurisubharmonic
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杨孝平, 韩燕苓
南京理工大学学报,2007,21(1):134~138,-0001,():
-1年11月30日
次黎曼测地线问题是变分学中的一个有约束的Lagrange问题,但在变分的过程中有个难点——如何推同的束条件“r'ED,在[a,b]上几乎处处成立”的解析式。该文从最优控制论的角度,将次黎曼测地线问题转化为一个最优控制问题,将约束条件r(t)ED转化为,进而得到了次黎曼Hamiltonian 的具体形式。同时将奇异曲线刻划为非正规极值曲线的投影。
次黎曼流形, 正规测地线, 奇异曲线
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杨孝平, 吕中学
应用数学学报,2007,30(2):279~288,-0001,():
-1年11月30日
本文研究定义在有界变差函数空间BD(Ω)上如下形式的各分泛函,得到了这个积分泛函关于L1强收敛的下关连续性结果。
有界变差函数空间BD (, Ω), , 积分泛函, 下半连续性
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【期刊论文】DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATHEODORY SPACES1
杨孝平, Song Yingqing, Yang Xiaoping, Liu Zhenhai
数学物理学报,2003,23(4):433~439,-0001,():
-1年11月30日
The aim of this paper is to get the decomposition of distrbutional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector flelds are of Carnot type. For this prupose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu=△u. Ln+Xu is proved, where u∈ BVx(Ω) adn denotes the approximate differential of u.
BV function,, C-C SPACE,, Radon ineasure,, vector field,, approximate differential
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【期刊论文】The chain rule and a compactness theorem for BV functions in the Heisenberg group Hn ☆
杨孝平, Ying-Qing Song a, b, ∗ and Xiao-Ping Yang b
J. Math. Anal. Appl. 287 (2003) 296-306,-0001,():
-1年11月30日
At first in the setting of the Heisenberg group we show the chain rule for a function u ∈ BVH(Ω) when composed with a Lipschitz function f :R→R and prove that v=f ◦ u belongs to BVH(Ω) and |DH v| |DH u|. More precisely the following result is shown: DHv=f (˜u)∇H uL2n+1 + 2ω2n−1 ω2n+1 f (u+)−f (u−) νuS Q−1 d Ju+f (˜u)Dc Hu. Secondly using the chain rule above we prove a compactness theorem for SBVH functions.
BVH function, Heisenberg group, Decomposition of a Radon measure, Chain rule, Compactness theorem
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