Metric character of Hamilton-Jacobi equations

被引：28

作者：

Siconolfi, A ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 355卷 / 05期

关键词：

Hamilton-Jacobi equations; viscosity solutions; distance functions;

D O I：

10.1090/S0002-9947-03-03237-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deal with the metrics related to Hamilton-Jacobi equations of eikonal type. If no convexity conditions are assumed on the Hamiltonian, these metrics are expressed by an inf-sup formula involving certain level sets of the Hamiltonian. In the case where these level sets are star-shaped with respect to 0, we study the induced length metric and show that it coincides with the Finsler metric related to a suitable convexification of the equation.

引用

页码：1987 / 2009

页数：23

共 14 条

[1]

[Anonymous], 1997, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

[2] ON HOPF FORMULAS FOR SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].

BARDI, M ;

EVANS, LC .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1984, 8 (11) :1373-1381

[3]

Barles G., 1994, Solutions de viscosite des equations de Hamilton-Jacobi, V17

[4]

BLUMENTHAL L., 1953, THEORY APPL DISTANCE

[5]

Busemann H., 1955, GEOMETRY GEODESICS

[6]

Busemann H., 1942, Metric Methods in Finsler Spaces and in the Foundations of Geometry

[7]

Camilli F, 1999, INDIANA U MATH J, V48, P1111

[8] Nonconvex degenerate Hamilton-Jacobi equations [J].

Camilli, F ;

Siconolfi, A .

MATHEMATISCHE ZEITSCHRIFT, 2002, 242 (01) :1-21

[9]

COURANT R, 1962, METHODS MATH PHYSICS, V2

[10] DIFFERENTIAL-GAMES AND REPRESENTATION FORMULAS FOR SOLUTIONS OF HAMILTON-JACOBI-ISAACS EQUATIONS [J].

EVANS, LC ;

SOUGANIDIS, PE .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1984, 33 (05) :773-797

← 1 2 →