Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians

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	Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians
	Zhao, Yinchuan 1,2; Tang, Tao 3,4; Wang, Jinghua 5
	2008-09-01
发表期刊	JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
ISSN	0219-8916
卷号	5 期号:3 页码:663-680
摘要	This paper is concerned with the Hamilton-Jacobi (HJ) equations of multidimensional space variables with convex Hamiltonians. Using Hopf's formula (I), we will study the differentiability of the HJ solutions. For any given point, we give a sufficient and necessary condition under which the solutions are C-k smooth in some neighborhood of the point. We also study the characteristics of the HJ equations. It is shown that there are only two kinds of characteristics, one never touches the singularity point, and the other touches the singularity point in a finite time. The sufficient and necessary condition under which the characteristic never touches the singularity point is given. Based on these results, we study the global structure of the set of singularity points for the HJ solutions. It is shown that there exists a one-to-one correspondence between the path connected components of the set of singularity points and the path connected components of a set on which the initial function does not attain its minimum. A path connected component of the set of singularity points never terminates at a finite time. Our results are independent of the particular forms of the equations as long as the Hamiltonians are convex.
关键词	Hamilton-Jacobi equations Hopf's formula (I) global structure singularity point
语种	英语
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000259233300008
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6802
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, Yinchuan
作者单位	1.Peking Univ, LMAM, Beijing 100871, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 4.Chinese Acad Sci, Inst Computat Math, Beijing, Peoples R China 5.Chinese Acad Sci, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Yinchuan,Tang, Tao,Wang, Jinghua. Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,2008,5(3):663-680.
APA	Zhao, Yinchuan,Tang, Tao,&Wang, Jinghua.(2008).Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians.JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS,5(3),663-680.
MLA	Zhao, Yinchuan,et al."Regularity and global structure of solutions to Hamilton-Jacobi equations I. Convex Hamiltonians".JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS 5.3(2008):663-680.