On the boundary values of harmonic functions
type: Item
instance of: scholarly article
title: On the boundary values of harmonic functions
zbMATH Open document ID: 0602.31005
DOI: 10.4171/RMI/10
published in: Revista Matemática Iberoamericana
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39319
review text: Let D be a domain with smooth boundary \(\partial D\) in the Euclidean space of dimension \(n\geq 3\). Given a continuous function w on \(\partial D\) with a continuous extension to D having a finite Dirichlet integral, it is known that the Dirichlet solution in D of f is the orthogonal projection of w onto the Hilbert space H of harmonic functions in D with finite Dirichlet integrals. Under hypotheses prescribed above the author shows that this orthogonal projection tends to w at all points of \(\partial D\) irrespective of the dimension n.
Mathematics Subject Classification ID: 31B25
zbMATH DE Number: 3971175
zbMATH Keywords: smooth boundary
zbMATH Keywords: finite Dirichlet integral
zbMATH Keywords: Dirichlet solution
zbMATH Keywords: Hilbert space
zbMATH Keywords: harmonic functions
zbMATH Keywords: orthogonal projection
author: Paul R. Garabedian
MaRDI profile type: Publication
OpenAlex ID: W2064238981
description: scientific article; zbMATH DE number 3971175