articles
2019-04-01
2019-04
https://link.springer.com/10.1007%2Fs11118-018-9684-8
Let X⊂ℝn be a bounded Lipschitz domain and consider the σ2-energy functional Fσ2[u;X]:=∫X∧2∇u2dx, over the space of admissible Sobolev maps A(X):=u∈W1,4(X,Sn−1):u|∂X=x|x|−1. In this article we address the question of multiplicity versus uniqueness for extremals and strong local minimisers of the σ2-energy funcional Fσ2[⋅,X] in A(X) where the domain X is n-dimensional annuli. We consider a topological class of maps referred to as spherical twists and examine them in connection with the Euler-Lagrange equations associated with σ2-energy functional over A(X), the so-called σ2-harmonic map equation on X. The main result is a surprising discrepancy between even and odd dimensions. In even dimensions the latter system of equations admits infinitely many smooth solutions amongst such maps whereas in odd dimensions this number reduces to one. The result relies on a careful analysis of the full versus the restricted Euler-Lagrange equations.
https://scigraph.springernature.com/explorer/license/
research_article
2019-04-11T12:38
327-345
Spherical Twists as the σ2-Harmonic Maps from n-Dimensional Annuli into Sn−1
false
en
Mathematical Sciences
0926-2601
Potential Analysis
1572-929X
50
Springer Nature - SN SciGraph project
debf896d8b0baab035dd4e01e15d1b66c0496cf9d1fca9db4f93638a637a1c20
readcube_id
3
dimensions_id
pub.1100751756
Department of Mathematics, University of Shahid Beheshti, Evin, Tehran, Iran
M. S.
Shahrokhi-Dehkordi
10.1007/s11118-018-9684-8
doi
Pure Mathematics