Martin Kruzik, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 4, CZ-182 08 Praha 8, Czech Republic, e-mail: kruzik@utia.cas.cz; Tomas Roubicek, Mathematical Institute, Charles University, Sokolovska 83, CZ-186 00 Praha 8, Czech Republic and Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 4, CZ-182 08 Praha 8, Czech Republic, e-mail: roubicek@karlin.mff.cuni.cz
Abstract: DiPerna and Majda generalized Young measures so that it is possible to describe "in the limit" oscillation as well as concentration effects of bounded sequences in $L^p$-spaces. Here the complete description of all such measures is stated, showing that the "energy" put at "infinity" by concentration effects can be described in the limit basically by an arbitrary positive Radon measure. Moreover, it is shown that concentration effects are intimately related to rays (in a suitable locally convex geometry) in the set of all DiPerna-Majda measures. Finally, a complete characterization of extreme points and extreme rays is established.
Keywords: bounded sequences in Lebesgue spaces, oscillations, concentrations, Young measures, DiPerna and Majda's measures, rays, extreme points, extreme rays
Classification (MSC2000): 28C15, 40A30
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