Sobolev maps with integer degree and applications to Skyrme’s problem
1992 ◽
Vol 436
(1896)
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pp. 197-201
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Let ɸ : R 3 → S 3 ⊂ R 4 , ∣ A ( ɸ )∣ 2 ═ Ʃ 3 α,β═1 │∂ ɸ /∂ x α ∧ ∂ ɸ /∂ x β ∣ 2 and let k ϵ Z . Skyrme's problem consists in minimizing the energy ε( ɸ ) : ═ ∫ R 3 ∣∇ ɸ ∣ 2 + ∣ A ( ɸ )∣ 2 d x among maps with degree k ═ d ( ɸ ) : ═ 1/2π 2 ∫ R 3 det ( ɸ , ∇ ɸ ) d x . We show that for all ɸ with finite energy d ( ɸ ) is an integer and then obtain existence of a minimizer of ε in the natural class of maps with finite energy.
2010 ◽
Vol 12
(01)
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pp. 121-181
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Keyword(s):
2010 ◽
Vol 12
(05)
◽
pp. 871-908
Keyword(s):
2002 ◽
Vol 7
(11)
◽
pp. 585-599
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1994 ◽
Vol 332
(1-2)
◽
pp. 129-135
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2012 ◽
Vol 27
(40)
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pp. 1250233
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Keyword(s):