Abstract
We show that any compact subset of Rd which is the closure of a bounded star-shaped Lipschitz domain Ω, such that ∁Ω 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. Kroó on C2 star-shaped domains.Moreover, we prove constructively the existence of an optimal AM for any K:=Ω¯⊂Rd where Ω is a bounded C1,1 domain. This is done by a particular multivariate sharp version of the Bernstein Inequality via the distance function.
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