USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS

被引：2617

作者：

CRANDALL, MG

ISHII, H

LIONS, PL

机构：

[1] CHUO UNIV,DEPT MATH,BUNKYO KU,TOKYO 112,JAPAN

[2] UNIV PARIS 09,CEREMADE,F-75576 PARIS 16,FRANCE

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 27卷 / 01期

关键词：

VISCOSITY SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; FULLY NONLINEAR EQUATIONS; ELLIPTIC EQUATIONS; PARABOLIC EQUATIONS; HAMILTON-JACOBI EQUATIONS; DYNAMIC PROGRAMMING; NONLINEAR BOUNDARY VALUE PROBLEMS; GENERALIZED SOLUTIONS; MAXIMUM PRINCIPLES; COMPARISON THEOREMS; PERRON METHOD;

D O I：

10.1090/S0273-0979-1992-00266-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking arguments. The range of important applications of these results is enormous. This article is a self-contained exposition of the basic theory of viscosity solutions.

引用

页码：1 / 67

页数：67

共 126 条

[1] ALEKSANDROV AD, 1968, VESTN LENINGR U MAT, V68, P89
[2] ALEKSANDROV AD, 1939, LENINGRAD U ANN, V37, P3
[3] [Anonymous], 1988, REV MAT IBER
[4] BAKEL' MAN I.Ya, 1961, SIBERIAN MATH J, V2, P179
[5] THE DYNAMIC-PROGRAMMING EQUATION FOR THE TIME-OPTIMAL CONTROL PROBLEM IN INFINITE DIMENSIONS
BARBU, V
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1991, 29 (02) : 445 - 456
[6] THE NECESSARY CONDITIONS FOR OPTIMAL-CONTROL IN HILBERT-SPACES
BARBU, V
BARRON, EN
JENSEN, R
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 133 (01) : 151 - 162
[7] BARDI M, 1990, COMMUN PART DIFF EQ, V15, P1649
[8] ON HOPF FORMULAS FOR SOLUTIONS OF HAMILTON-JACOBI EQUATIONS
BARDI, M
EVANS, LC
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1984, 8 (11) : 1373 - 1381
[9] BARLES G, 1985, ANN I H POINCARE-AN, V2, P21
[10] WAVE-FRONT PROPAGATION FOR REACTION-DIFFUSION SYSTEMS OF PDE
BARLES, G
EVANS, LC
SOUGANDIS, PE
[J]. DUKE MATHEMATICAL JOURNAL, 1990, 61 (03) : 835 - 858

← 1 2 3 4 5 6 7 8 9 10 →