On the regularity of boundary points in potential theory
Halsey L. Royden · Proceedings of the American Mathematical Society · 1952
A unique harmonic function u may be constructed from the given boundary values by any of several methods, for example, by exhausting G with a sequence of domains for which the Dirichlet problem is solvable [3],1 by using subharmonic functions [4], or by the Dirichlet principle [1; 5]. There then arises the question of whether the relation (1) holds for our function u or not. This leads us to the following definition: A point Po of R is said to be regular for the Dirichlet problem if for every set of continuous boundary values f(P) we always have