Mathematics ( IF 1.747 ) Pub Date : 2020-08-01 , DOI: 10.3390/math8081262
Zdzisław Dzedzej; Tomasz Gzella

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.

down
wechat
bug