Geodesic
On the measures of DiPerna and Majda
Mathematica Bohemica, Tome 122 (1997) no. 4, pp. 383-399
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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.
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.
DOI : 10.21136/MB.1997.126212
Classification : 28C15, 40A30, 46N10, 49Q20
Keywords: bounded sequences in Lebesgue spaces; oscillations; Young measures; DiPerna and Majda measures; rays; extreme points; extreme rays; concentrations 
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Kružík, Martin; Roubíček, Tomáš. On the measures of DiPerna and Majda. Mathematica Bohemica, Tome 122 (1997) no. 4, pp. 383-399. doi: 10.21136/MB.1997.126212

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