| Global Structure and Regularity of Solutions to the Eikonal Equation | |
Li, Tian-Hong1,2 ; Wang, JingHua1; Wen, HaiRui3
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| 2019-05-01 | |
| Source Publication | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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| ISSN | 0003-9527 |
| Volume | 232Issue:2Pages:1073-1112 |
| Abstract | 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 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11471332] ; National Natural Science Foundation of China[10931007] ; National Natural Science Foundation of China[11771429] |
| WOS Research Area | Mathematics ; Mechanics |
| WOS Subject | Mathematics, Applied ; Mechanics |
| WOS ID | WOS:000462144500011 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34211 |
| Collection | 数学所 |
| Corresponding Author | Li, Tian-Hong |
| Affiliation | 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 |
| Recommended Citation 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. |
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