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

"Det vs det"

Abstract

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

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