TY - JOUR
T1 - Approximation of Flat W-2,W-2 Isometric Immersions by Smooth Ones
AU - Hornung, Peter
PY - 2011/3
Y1 - 2011/3
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=79951813152&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1007/s00205-010-0374-y
U2 - 10.1007/s00205-010-0374-y
DO - 10.1007/s00205-010-0374-y
M3 - Article
SN - 0003-9527
VL - 199
SP - 1015
EP - 1067
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 3
ER -