Approximation by harmonic functions and the Dirichlet problem. (English) Zbl 0759.41033

Netuka, I.

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.

MSC:

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

Keywords:

harmonic approximation; Perron-Wiener-Brelot solutions; Dirichlet problem

Citations:

Zbl 0744.00033