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On the singular support of the distributional determinant.
- Source :
-
Annales de l'Institut Henri Poincaré C . Nov2016, Vol. 10 Issue 6, p657-696. 40p. - Publication Year :
- 2016
-
Abstract
- Let Ω ⊂ ℝ n be bounded and open, let p ≧ n 2 /( n + 1) and let u : Ω → ℝ n be in the Sobolevspace W 1, n (Ω; ℝ n ). This paper discusses the singular part of the distributional determinant Det D u and shows the existence of functions u for which that singular part is supported in a set of prescribed Hausdorff-dimension α ∈ (0, n ). For n = 2 and simply connected Ω the problem is equivalent to analyzing div ( bv ) − b . D v where v ∈ W 1, p (Ω; ℝ 2 ) with div b = 0. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02941449
- Volume :
- 10
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Annales de l'Institut Henri Poincaré C
- Publication Type :
- Academic Journal
- Accession number :
- 121130676
- Full Text :
- https://doi.org/10.1016/S0294-1449(16)30201-3