Abstract:Let U be a bounded open set of the Euclidean space R d and let H(U) denote the space of all real-valued continuous functions on U that are harmonic on U. We present a sufficient condition on the set ∂ reg U of all regular points of U that ensures that H(U) is complemented in C U . We also present examples showing that this condition is not necessary. The proof of the positive result is based upon a general result on complementability of a simplicial function space in a C(K) space.
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.