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

  • Paolo Caldiroli
  • Giulia Treu
Article

Abstract

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}.

Keywords

Initial Data Uniqueness Property Measure Property Measure Zero Generalize Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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