Approximating the solutions of differential inclusions driven by measures

The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of un...

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Bibliographic Details
Published in:Annali di matematica pura ed applicata 2019-12, Vol.198 (6), p.2123-2140
Main Authors: Di Piazza, L., Marraffa, V., Satco, B.
Format: Article
Language:English
Subjects:
Approximation
Inclusions
Mathematics
Mathematics and Statistics
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Summary:The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of uniformly bounded ε -variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-019-00857-6