Eikonal equations on ramified spaces

被引：9

作者：

Camilli, Fabio ^{[1
]}

Schieborn, Dirk

Marchi, Claudio ^{[2
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, I-00161 Rome, Italy

[2] Univ Padua, Dip Matemat, I-35121 Padua, Italy

来源：

INTERFACES AND FREE BOUNDARIES | 2013年 / 15卷 / 01期

关键词：

Hamilton-Jacobi equation; ramified space; viscosity solution; comparison principle; HAMILTON-JACOBI EQUATIONS;

D O I：

10.4171/IFB/297

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We generalize the results in [23] to higher dimensional ramified spaces. For this purpose we introduce ramified manifolds and, as special cases, locally elementary polygonal ramified spaces (LEP spaces). On LEP spaces we develop a theory of viscosity solutions for Hamilton-Jacobi equations, providing existence and uniqueness results.

引用

页码：121 / 140

页数：20

共 25 条

[1] Achdou Y., NODEA NONL IN PRESS
[2] ALVAREZ O., 2010, MEM AM MATH SOC, V204
[3] Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds
Azagra, D
Ferrera, J
López-Mesas, F
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 220 (02) : 304 - 361
[4] Bardi M., 1997, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations, with Appendices by Falcone M and Soravia P, DOI DOI 10.1007/978-0-8176-4755-1
[5] Barles G., PREPRINT
[6] Bressan A, 2007, NETW HETEROG MEDIA, V2, P313
[7] Camilli F., 2011, ARXIV11055725
[8] Cannarsa P, 2004, J EUR MATH SOC, V6, P435
[9] Homogenization and Enhancement for the G-Equation
Cardaliaguet, P.
Nolen, J.
Souganidis, P. E.
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 199 (02) : 527 - 561
[10] Existence of C1 critical subsolutions of the Hamilton-Jacobi equation
Fathi, A
Siconolfi, A
[J]. INVENTIONES MATHEMATICAE, 2004, 155 (02) : 363 - 388

← 1 2 3 →