Approximation of Flat W-2,W-2 Isometric Immersions by Smooth Ones

Peter Hornung

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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).
Original languageEnglish
Pages (from-to)1015-1067
Number of pages53
JournalArchive for Rational Mechanics and Analysis
Volume199
Issue number3
DOIs
Publication statusPublished - Mar 2011

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Isometric Immersion
del operator
Partial derivative
Derivatives
Lipschitz Domains
Continuously differentiable
Approximation
Regularity Conditions
Bounded Domain
Closure
Infinity
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Approximation of Flat W-2,W-2 Isometric Immersions by Smooth Ones. / Hornung, Peter.

In: Archive for Rational Mechanics and Analysis, Vol. 199, No. 3, 03.2011, p. 1015-1067.

Research output: Contribution to journalArticle

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