On the singular support of the distributional determinant.

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]