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-Hong1,2 ; Wang, JingHua 1; Wen, HaiRui 3
	2019-05-01
发表期刊	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN	0003-9527
卷号	232 期号:2 页码:1073-1112
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.
DOI	10.1007/s00205-018-01339-4
语种	英语
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
WOS类目	Mathematics, Applied ; Mechanics
WOS记录号	WOS:000462144500011
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34211
专题	数学所
通讯作者	Li, Tian-Hong
作者单位	1.Chinese Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sinica, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 3.Beijing Inst Technol, Dept Math, Beijing 100081, 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.