

Preprint 93/2003
A new approach to counterexamples to L1 estimates: Korn’s inequality, geometric rigidity, and regularity for gradients of separately convex functions
Sergio Conti, Daniel Faraco, and Francesco Maggi
Contact the author: Please use for correspondence this email.
Submission date: 21. Nov. 2003
Pages: 17
published in: Archive for rational mechanics and analysis, 175 (2005) 2, p. 287-300
DOI number (of the published article): 10.1007/s00205-004-0350-5
Bibtex
Download full preprint: PDF (192 kB), PS ziped (185 kB)
Abstract:
The derivation of counterexamples to estimates can
be reduced to a geometric decomposition procedure along rank-one lines
in matrix space.
We illustrate this concept in
two concrete applications.
Firstly, we recover a celebrated, and rather
complex, counterexample by Ornstein, proving
the failure of Korn's inequality, and of the corresponding geometrically nonlinear
rigidity result, in
. Secondly, we construct a function
which is
separately convex but whose gradient is not in
,
in the sense that the mixed derivative
is not a bounded measure.