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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree

Abstract

Consider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn 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 Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient mappings

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Category:
Articles
Type:
artykuły w czasopismach
Published in:
Mathematics no. 8,
ISSN: 2227-7390
Language:
English
Publication year:
2020
Bibliographic description:
Dzedzej Z., Gzella T.: Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree// Mathematics -Vol. 8,iss. 8 (2020), s.1262-
DOI:
Digital Object Identifier (open in new tab) 10.3390/math8081262
Verified by:
Gdańsk University of Technology

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