TY - JOUR
T1 - On the Jäger-Kaul theorem concerning harmonic maps
AU - Hong, Min Chun
PY - 2000/1
Y1 - 2000/1
N2 - In 1983, Jäger and Kaul proved that the equator map u*(x) = (x/|x|, 0) : Bn → Sn is unstable for 3 ≤ n ≤ 6 and a minimizer for the energy functional E(u, Bn) = ∫Bn |∇u|2dx in the class H1,2(Bn, Sn) with u = u* on ∂ Bn when n ≥ 7. In this paper, we give a new and elementary proof of this Jäger-Kaul result. We also generalize the Jäger-Kaul result to the case of p-harmonic maps.
AB - In 1983, Jäger and Kaul proved that the equator map u*(x) = (x/|x|, 0) : Bn → Sn is unstable for 3 ≤ n ≤ 6 and a minimizer for the energy functional E(u, Bn) = ∫Bn |∇u|2dx in the class H1,2(Bn, Sn) with u = u* on ∂ Bn when n ≥ 7. In this paper, we give a new and elementary proof of this Jäger-Kaul result. We also generalize the Jäger-Kaul result to the case of p-harmonic maps.
UR - http://www.scopus.com/inward/record.url?scp=0013198067&partnerID=8YFLogxK
U2 - 10.1016/S0294-1449(99)00103-1
DO - 10.1016/S0294-1449(99)00103-1
M3 - Article
SN - 0294-1449
VL - 17
SP - 35
EP - 46
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 1
ER -