Optimal polynomial admissible meshes on some classes of compact subsets of R-d

摘要

We show that any compact subset of R-d which is the closure of a bounded star-shaped Lipschitz domain Omega, such that subset of Omega has positive reach in the sense of Federer, admits an optimal AM (admissible mesh), that is a sequence of polynomial norming sets with optimal cardinality. This extends a recent result of A. Kroo on l(2) star-shaped domains.