Approximating the solutions of differential inclusions driven by measures

  • L. Di Piazza
  • V. MarraffaEmail author
  • B. Satco


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 \(\varepsilon \)-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.


Differential inclusions BV functions \(\varepsilon \)-Variations Regulated functions 

Mathematics Subject Classification

Primary 26A45 Secondary 34A60 28B20 34A12 26A42 



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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of PalermoPalermoItaly
  2. 2.Faculty of Electrical Engineering and Computer Science, Integrated Center for Research, Development and Innovation in Advanced Materials, Nanotechnologies, and Distributed Systems for Fabrication and Control (MANSiD)Stefan cel Mare University of SuceavaSuceavaRomania

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