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.

Time-dependent systems of generalized young measures

De Simone, Antonio;
2007

Abstract

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.
2007
Settore MAT/05 - Analisi Matematica
Absolute continuity; bounded variation; concentration and oscillation effects; weak derivatives; young measures
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/84002
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