Harmonic maps with potential

被引：0
作者：
Ali Fardoun
Andrea Ratto
机构：
[1] University of Brest,Department of Mathematics
[2] Unical,Dipartimento di Matematica
来源：
Calculus of Variations and Partial Differential Equations | 1997年 / 5卷
关键词：
58E20; 49A10; 35J20; Harmonic maps; the Landau-Lifshitz equation; the Neumann motion;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let (M,g) and (N,h) be two Riemannian manifolds, and G : N → ℝ a given function. If f : M → N is a smooth map, we set EG(f)=1/2 ∫M[|df|2 − 2G(f)]dvg. We establish some variational properties and some existence results for the functional EG(f): in particular, we analyse the case of maps into a sphere.
引用
收藏
页码：183 / 197
页数：14
相关论文
共 50 条
[11]   Stability of -Harmonic Maps [J].
Pirbodaghi, Zahra ;
Rezaii, Morteza Mirmohammad ;
Torbaghan, Seyed Mehdi Kazemi .
MATHEMATICS, 2018, 6 (06)
[12]   A note on harmonic maps [J].
Liu, H ;
Liao, G .
APPLIED MATHEMATICS LETTERS, 1996, 9 (04) :95-97
[13]   ON THE GENERALIZED OF HARMONIC AND BI-HARMONIC MAPS [J].
Djaa, M. ;
Cherif, A. M. ;
Zegga, K. ;
Ouakkas, S. .
INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, 2012, 5 (01) :90-100
[14]   On the nonexistence of harmonic and bi-harmonic maps [J].
Cherif, Ahmed Mohammed .
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2025, 68 (02) :173-184
[15]   Sobolev spaces of maps and the Dirichlet problem for harmonic maps [J].
Pigola, Stefano ;
Veronelli, Giona .
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2019, 21 (01)
[16]   Some results on harmonic and bi-harmonic maps [J].
Cherif, Ahmed Mohammed .
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2017, 14 (07)
[17]   Diagrams and harmonic maps, revisited [J].
Pacheco, Rui ;
Wood, John C. .
ANNALI DI MATEMATICA PURA ED APPLICATA, 2023, 202 (03) :1051-1085
[18]   Approximation of fractional harmonic maps [J].
Antil, Harbir ;
Bartels, Soren ;
Schikorra, Armin .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2023, 43 (03) :1291-1323
[19]   Harmonic maps and cosymplectic manifolds [J].
Boeckx, E ;
Gherghe, C .
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2004, 76 :75-92
[20]   COMPUTING HARMONIC MAPS AND CONFORMAL MAPS ON POINT CLOUDS [J].
Wu, Tianqi ;
Yau, Shing-Tung .
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2023, 41 (05) :880-909
12345