Minimizing energy among homotopic maps
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204305053 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |