C1 mappings in R5 with derivative of rank at most 3 cannot be uniformly approximated by C2 mappings with derivative of rank at most 3

[摘要] We find a counterexample to a conjecture of Galeski [1] by constructing for some positive integers m < n a mapping f is an element of C-1(R-n,R-n) satisfying rank D f <= m that, even locally, cannot be uniformly approximated by C-2 mappings f, satisfying the same rank constraint: rank D f(epsilon) <= m. (C) 2018 Elsevier Inc. All rights reserved.

[发布日期] 2018-12-15

[关键词] Approximation by smooth mappings;Rank of the derivative;Sard's theorem