Global Structure and Regularity of Solutions to the Eikonal Equation

doi:10.1007/s00205-018-01339-4

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	Global Structure and Regularity of Solutions to the Eikonal Equation
	Li, Tian-Hong2,3 ; Wang, JingHua 2; Wen, HaiRui 1
刊名	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
	2019-05-01
卷号	232 期号:2 页码:1073-1112
ISSN号	0003-9527
DOI	10.1007/s00205-018-01339-4
英文摘要	The evolutionary Eikonal equation is a Hamilton-Jacobi equation with Hamiltonian H(P)=vertical bar P vertical bar, which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly convex Hamiltonians, therefore leading to new phenomena. In this paper, we study the set of singularity points of solutions in the upper half space for C-1 or C-2 initial data, with emphasis on the countability of connected components of the set. The regularity of solutions in the complement of the set of singularity points is also obtained.
资助项目	National Natural Science Foundation of China[11471332] ; National Natural Science Foundation of China[10931007] ; National Natural Science Foundation of China[11771429]
WOS研究方向	Mathematics ; Mechanics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000462144500011
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34210]
专题	数学所
通讯作者	Li, Tian-Hong
作者单位	1.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 2.Chinese Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sinica, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Tian-Hong,Wang, JingHua,Wen, HaiRui. Global Structure and Regularity of Solutions to the Eikonal Equation[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2019,232(2):1073-1112.
APA	Li, Tian-Hong,Wang, JingHua,&Wen, HaiRui.(2019).Global Structure and Regularity of Solutions to the Eikonal Equation.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,232(2),1073-1112.
MLA	Li, Tian-Hong,et al."Global Structure and Regularity of Solutions to the Eikonal Equation".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 232.2(2019):1073-1112.