zbMATH — the first resource for mathematics

Approximation by harmonic functions and the Dirichlet problem. (English) Zbl 0759.41033
Approximation by solutions of partial differential equations, Proc. NATO Adv. Res. Workshop, Hanstholm/Den. 1991, NATO ASI Ser., Ser. C 365, 155-168 (1992).
Summary: [For the entire collection see Zbl 0744.00033.]
The purpose of this paper is to give a survey of several results on harmonic approximation in classical as well as abstract potential theory. Section 1 recalls basic notions of the theory of harmonic spaces representing a good framework for the subject under consideration. In Section 2 the question of approximation of harmonic functions by single layer potentials is investigated. Section 3 deals with pervasive function spaces and harmonic approximation. Finally, Section 4 is devoted to approximation of Perron-Wiener-Brelot solutions by solutions of the classical Dirichlet problem.

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
Zbl 0744.00033