International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 30, Pages 1599-1611
doi:10.1155/S0161171204305053
Minimizing energy among homotopic maps
Department of Mathematics, Stanford University, Palo Alto 94305, CA, USA
Received 6 May 2003
Copyright © 2004 Pengzi Miao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study an energy minimizing sequence {ui} in a fixed
homotopy class of smooth maps from a 3-manifold. After deriving
an approximate monotonicity property for {ui} and a
continuous version of the Luckhaus lemma (Simon, 1996) on S2, we
show that, passing to a subsequence, {ui} converges strongly
in W1,2 topology wherever there is small energy
concentration.