Weak compactness of wave maps and harmonic maps (Q1276063)
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scientific article; zbMATH DE number 1240518
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weak compactness of wave maps and harmonic maps |
scientific article; zbMATH DE number 1240518 |
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Weak compactness of wave maps and harmonic maps (English)
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8 November 1999
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By exploiting the Hodge structure related to harmonic maps, \({\mathcal H}^1\) estimates for Jacobians, \({\mathcal H}^1\)-BMO (bounded mean oscillation) duality, a hyperbolic monotonicity formula and the concentration compactness method, the authors show that a weak limit of a sequence of wave maps in \((1+2)\) dimensions with uniformly bounded energy is again a wave map. They also show that translating the ideas to the elliptic situation gives a much shorter proof of the results of \textit{F. Bethuel} [Calc. Var. Partial Differ. Equ. 1, No. 3, 267-310 (1993; Zbl 0812.58018)] on Palais-Smale sequences for the harmonic map functional on two dimensional domains and on limits of almost \(H\)-surfaces.
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wave maps
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Hodge structure
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weak limits
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Palais-Smale sequences
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harmonic map functional
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limits of almost \(H\)-surfaces
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0.9206424
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0.8992466
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0.89682305
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0.8924724
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0.8920352
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