A fractional version of Rivière's GL(n)-gauge
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Date
2022-08
Publication Type
Journal Article
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Abstract
We prove that for antisymmetric vector field Ω with small L²-norm there exists a gauge A ∈ L∞ ∩ Ẇ(1/2,2)(ℝ¹, GL(N)) such that
div(1/2)(AΩ − d(1/2)A) = 0.
This extends a celebrated theorem by Rivière to the nonlocal case and provides conservation laws for a class of nonlocal equations with antisymmetric potentials, as well as stability under weak convergence.
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published
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Journal / series
Volume
201 (4)
Pages / Article No.
1817 - 1853
Publisher
Springer
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Subject
Fractional divergence; Fractional div-curl lemma; Fractional harmonic maps
Organisational unit
08819 - Da Lio, Francesca (Tit.-Prof.)
Notes
Funding
192062 - Variational Analysis in Geometry (SNF)