International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 485096 | https://doi.org/10.1155/S0161171204305053

Pengzi Miao, "Minimizing energy among homotopic maps", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 485096, 13 pages, 2004. https://doi.org/10.1155/S0161171204305053

Minimizing energy among homotopic maps

Received06 May 2003

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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