

Preprint 78/2007
Approximation of W2,2 isometric immersions by smooth isometric immersions
Peter Hornung
Contact the author: Please use for correspondence this email.
Submission date: 03. Sep. 2007 (revised version: September 2010)
Pages: 48
published in: Archive for rational mechanics and analysis, 199 (2011) 3, p. 1015-1067
DOI number (of the published article): 10.1007/s00205-010-0374-y
Bibtex
Abstract:
Part I: This is the first of two papers in which we study
isometric immersions u from a flat domain
into R3.
Here we study the geometry of the set on which
is locally
constant and the
properties of local line of curvature parametrizations for nonconvex S.
A main result is that u(S) can be approximated by flat surfaces
consisting of finitely many
planar regions and finitely many developable regions.
In a companion paper we will use this to prove that, for a large class
of domains S, the
strong
closure of the set of isometric immersions lying in
agrees with the set of all
isometric immersions.
Part II: Let be a bounded Lipschitz domain and denote by
the set of mappings
which satisfy
almost everywhere.
Under an additional regularity condition on the boundary
(which
is satisfied if
is piecewise continuously differentiable)
we prove that
the strong
closure of
agrees with
.
Download papers: Part I (PDF, 692 kB), Part II (PDF, 434 kB)