Abstract
The talk is based on my joint work with Jan Maly:
``Approximation in Sobolev spaces of nonlinear expressions involving
the gradient". Ark. Math. 40 (2002), 245-274.
We investigate a problem of approximation of a large class of nonlinear
expressions
, including polyconvex functions, that appear in
calculus of variations. Here
is a mapping from the Sobolev space
. In particular, when
, we obtain an approximation by
mappings which, from the point of view of applications, are almost as good
as Lipschitz mappings. As far as we know, for nonlinear problems that we
consider, no natural approximation results were known before. The results
about the approximation of
are consequences of the main result
of the paper on a very strong approximation of Sobolev functions by
locally weakly monotone functions.
TUESDAY, October 19, 2004
Time: 1:30 P.M.
Location: PPB 300