ON THE RAYLEIGH QUOTIENT AND THE FIRST EIGENVALUE FOR SOME VECTOR-VALUED VARIATIONAL PROBLEMS

被引：0

作者：

Brock, Friedemann ^{[1
]}

Manasevich, R. ^{[2
]}

机构：

[1] Univ Chile, Fac Ciencias, Dept Matemat, Santiago, Chile

[2] Univ Chile, Ctr Modelamiento Matemat, Dept Ingn Matemat, Santiago, Chile

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2007年 / 20卷 / 04期

关键词：

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the first eigenvalue of a vector-valued p-Laplacian problem is equal to the first eigenvalue of the corresponding scalar p-Laplacian, and that the components of its first eigenvectors are merely copies of the first eigenfunction of the scalar problem. We also show variants of this result for some other homogeneous vector-valued problems.

引用

页码：429 / 443

页数：15

共 50 条

[1] SOME MINIMAX PROBLEMS OF VECTOR-VALUED FUNCTIONS
TANAKA, T
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1988, 59 (03) : 505 - 524
[2] Vector-valued variational principles
Finet, C
Quarta, L
Troestler, C
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (01) : 197 - 218
[3] THE STRUCTURE OF EXTREMALS OF AUTONOMOUS VARIATIONAL PROBLEMS WITH VECTOR-VALUED FUNCTIONS
Zaslavski, Alexander J.
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2006, 19 (10) : 1177 - 1200
[4] VARIATIONAL PROBLEMS WITH OBSTACLES AND INTEGRAL CONSTRAINTS FOR VECTOR-VALUED FUNCTIONS
HILDEBRANDT, S
MEIER, M
MANUSCRIPTA MATHEMATICA, 1979, 28 (1-3) : 185 - 206
[5] VECTOR-VALUED LOCAL MINIMIZERS OF NONCONVEX VARIATIONAL-PROBLEMS
STERNBERG, P
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1991, 21 (02) : 799 - 807
[6] SINGULAR PERTURBATIONS OF VARIATIONAL-PROBLEMS OF VECTOR-VALUED FUNCTIONS
ISHIGE, K
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1994, 23 (11) : 1453 - 1466
[7] A nonintersection property for extremals of variational problems with vector-valued functions
Zaslavski, Alexander J.
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (06): : 929 - 948
[8] Turnpike property for extremals of variational problems with vector-valued functions
Zaslavski, AJ
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (01) : 211 - 231
[9] THE REGULARITY OF SOME VECTOR-VALUED VARIATIONAL INEQUALITIES WITH GRADIENT CONSTRAINTS
Safdari, Mohammad
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (02) : 413 - 428
[10] VARIATIONAL INEQUALITIES FOR VECTOR-VALUED FUNCTIONS
HILDEBRANDT, S
WIDMAN, KO
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1979, 309 : 191 - 220

← 1 2 3 4 5 →