Approximation of Flat W2,2 Isometric Immersions by Smooth Ones

Let S subset of R-2 be a bounded Lipschitz domain and denote by W-iso(2,2) (S; R-3) the set of mappings u is an element of W-2,W-2 (S; (3)) which satisfy (del u)(T) (del u) = Id almost everywhere. Under an additional regularity condition on the boundary partial derivative S (which is satisfied if partial derivative S is piecewise continuously differentiable), we prove that the strong W-2,W-2 closure of W-iso(2,2) (S; R-3) boolean AND C-infinity((S) over bar; R-3) agrees with W-iso(2,2) (S; R-3).