Relaxation of Hamilton-Jacobi equations

被引：4
作者：
Ishii, H
Loreti, P
机构：
[1] Waseda Univ, Sch Educ, Dept Math, Shinjuku Ku, Tokyo 1698050, Japan
[2] Univ Roma La Sapienza, Dipartimento Metodi & Modelli Matemat, I-00161 Rome, Italy
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2003年 / 169卷 / 04期
关键词：
D O I：
10.1007/s00205-003-0268-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the relaxation of Hamilton-Jacobi equations. The relaxation in our terminology is the following phenomenon: the pointwise supremum over a certain collection of subsolutions, in the almost everywhere sense, of a Hamilton-Jacobi equation yields a viscosity solution of the ``convexified'' Hamilton-Jacobi equation. This phenomenon has recently been observed in [13] in eikonal equations. We show in this paper that this relaxation is a common phenomenon for a wide range of Hamilton-Jacobi equations.
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页码：265 / 304
页数：40
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