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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree

Author

Listed:
  • Zdzisław Dzedzej

    (Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland)

  • Tomasz Gzella

    (Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland)

Abstract

Consider the Euclidean space R n with the orthogonal action of a compact Lie group G . We prove that a locally Lipschitz G -invariant mapping f from R n to R can be uniformly approximated by G -invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarkés generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient mappings.

Suggested Citation

  • Zdzisław Dzedzej & Tomasz Gzella, 2020. "Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1262-:d:393226
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