Carnegie Mellon
Department of Mathematical 

Irene Fonseca, Department of Mathematical Sciences, Carnegie Mellon University.

"Det vs det"


Sharp results for weak convergence of the determinant jacobian are given using a new isoperimetric inequality. It is shown that if $u_n \in W^{1,N}(\Omega;\mathbb{R}^N)$, $u_n \rightharpoonup u$ in $W^{1,N-1}(\Omega;\mathbb{R}^N)$, where $\Omega$ is a bounded, open subset of $\mathbb{R}^N$, and if $\{{\rm det}\, \nabla u_n\}$ converges weakly-* in the sense of measures to a Radon measure $\mu$, then $\frac{d \mu}{d
\mathcal L^N}={\rm det}\, \nabla u$ a.e. in $\Omega$.

This is joint work with Giovanni Leoni and Jan Malý.

TUESDAY, October 1, 2002
Time: 1:30 P.M.
Location: PPB 300