Minimizing energy among homotopic maps

Pengzi Miao

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-13

Abstract:

We study an energy minimizing sequence { u i } in a fixed homotopy class of smooth maps from a 3 -manifold. After deriving an approximate monotonicity property for { u i } and a continuous version of the Luckhaus lemma (Simon, 1996) on S 2 , we show that, passing to a subsequence, { u i } converges strongly in W 1 , 2 topology wherever there is small energy concentration.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:485096

DOI: 10.1155/S0161171204305053

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