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Moduli of continuity of selections from nonconvex maps

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Abstract

We consider two continuous selection problems related to the differential inclusion\(\dot x\) ∈F(t, x). Assuming thatF is Hölder or Lipschitz continuous with compact, not necessarily convex values, we provide estimates on the modulus of continuity of these selections.

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References

  1. Antosiewicz, H.A. and Cellina, A., Continuous selections and differential relations,J. Differential Equations 19 (1975), 386–398.

    Google Scholar 

  2. Aubin, J.P. and Cellina, A.,Differential Inclusions, Springer-Verlag, Berlin, 1984.

    Google Scholar 

  3. Bressan, A., Directionally continuous selections and differential inclusions,Funkcial Ekvac. 31 (1988), 459–470.

    Google Scholar 

  4. Bressan, A., Selections of Lipschitz multifunctions generating a continuous flow,Differential Integral Equations 4 (1991), 483–490.

    Google Scholar 

  5. Bressan, A. and Colombo, G., Extensions and selections of maps with decomposable values,Studia Math. 40 (1988), 69–86.

    Google Scholar 

  6. Bressan, A., Cellina, A. and Fryszkowski, A., A class of absolute retracts in the spaceL 1,Proc. Amer. Math. Soc. 112 (1991), 413–418.

    Google Scholar 

  7. Cellina, A., On the set of solutions to Lipschitzian differential inclusions,Differential Integral Equations 1 (1988), 495–500.

    Google Scholar 

  8. Fryszkowski, A., Continuous selections for a class of non-convex multivalued maps,Studia Math. 76 (1983), 163–174.

    Google Scholar 

  9. LeDonne, A. and Marchi, M.V., Representation of Lipschitzian compact convex valued mappings,Rend. Accad. Naz. Lincei 68 (1980), 278–280.

    Google Scholar 

  10. Pucci, A., Sistemi di equazioni differenziali con secondo membro discontinuo rispetto all'incognita,Rend. Istit. Mat. Univ. Trieste 3 (1971), 75–80.

    Google Scholar 

  11. Vitale, R.A., The Steiner point in infinite dimensions,Israel J. Math. 52 (1985), 245–250.

    Google Scholar 

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Authors and Affiliations

  1. SISSA, Via Beirut 4, 34014, Trieste, Italy

    Alberto Bressan

  2. Department of Mathematics, University of Colorado, 80309, Boulder, CO, USA

    Fabio Ancona

Authors
  1. Alberto Bressan
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  2. Fabio Ancona
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Bressan, A., Ancona, F. Moduli of continuity of selections from nonconvex maps. Set-Valued Anal 1, 47–63 (1993). https://doi.org/10.1007/BF01039290

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  • DOI: https://doi.org/10.1007/BF01039290

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