Measure properties of the set of initial data yielding non uniqueness for a class of differential inclusions

  • Paolo Caldiroli
  • Giulia Treu


We study uniqueness property for the Cauchy problemx′∈ϖV(x), x(0)=ξ, whereVRn→R is a locally Lipschitz continuous, quasiconvex function (i.e. the sublevel sets {V≤c} are convex) and ϖV(x) is the generalized gradient ofV atx. We prove that if 0∉ϖV(x) forV(x)≥b, then the set of initial data ξ∈{V=b} yielding non uniqueness of solution in a geometric sense has (n−1)-dimensional Hausdorff measure zero in {V=b}.


Initial Data Uniqueness Property Measure Property Measure Zero Generalize Gradient 
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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Paolo Caldiroli
    • 1
  • Giulia Treu
    • 2
  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Dipartimento di Matematica e InformaticaUniversità di UdineUdineItaly

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