Superposition Principle for Differential Inclusions

  • Giulia Cavagnari
  • Antonio MarigondaEmail author
  • Benedetto Piccoli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)


We prove an extension of the Superposition Principle by Ambrosio-Gigli-Savaré in the context of a control problem. In particular, we link the solutions of a finite-dimensional control system, with dynamics given by a differential inclusion, to a solution of a continuity equation in the space of probability measures with admissible vector field. We prove also a compactness and an approximation result for admissible trajectories in the space of probability measures.


Continuity equation Differential inclusions Optimal transport Superposition principle 



The authors acknowledge the endowment fund of the Joseph and Loretta Lopez Chair and the support of the INdAM-GNAMPA Project 2016 Stochastic Partial Differential Equations and Stochastic Optimal Transport with Applications to Mathematical Finance.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Giulia Cavagnari
    • 1
  • Antonio Marigonda
    • 2
    Email author
  • Benedetto Piccoli
    • 1
  1. 1.Department of Mathematical SciencesRutgers University - CamdenCamdenUSA
  2. 2.Department of Computer SciencesUniversity of VeronaVeronaItaly

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