Time-dependent systems of generalized Young measures

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March 2007, 2(1): 1-36. doi: 10.3934/nhm.2007.2.1

Time-dependent systems of generalized Young measures

G. Dal Maso ^1, , Antonio DeSimone ^2, , M. G. Mora ^3, and M. Morini ^1,

1.	SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014, Trieste, Italy, Italy
2.	SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste, Italy
3.	SISSA-International School for Advanced Studies, Via Beirut 2-4,, 34014, Trieste, Italy

Received July 2006 Revised September 2006 Published December 2006

Abstract
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In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows us to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.

Keywords: absolute continuity, concentration and oscillation effects, Young measures, bounded variation, weak derivatives.

Mathematics Subject Classification: Primary: 28A33, 49Q20, 26A4.

Citation: G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini. Time-dependent systems of generalized Young measures. Networks & Heterogeneous Media, 2007, 2 (1) : 1-36. doi: 10.3934/nhm.2007.2.1

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