Institute of Information Theory and Automation
Academy of Sciences of the Czech Republic
Pod vodárenskou vezí 4, CZ-182 08 Praha 8, Czech Republic.
"Oscillations and Concentrations in Sequences of Gradients"
It is well-known that Morrey's quasiconvexity is closely related to gradient Young measures, i.e., Young measures generated by sequences of gradients in . Concentration effects, however, cannot be treated by Young measures. One way how to describe both oscillation and concentration effects in a fair generality are the so-called DiPerna-Majda measures.
DiPerna and Majda showed that having a sequence bounded in
, and a complete separable subring of continuous bounded functions on
then there exists a subsequence of (not relabeled),
a positive Radon measure on , and a family of probability
(the metrizable compactification of
corresponding to ),
, such that
where . Our talk will address the question: What conditions must satisfy, so that for with on ? We are going to state necessary and sufficient conditions. We will mainly work with , however, special cases for will be discussed, as well.
TUESDAY, April 25, 2006