Abstract: In this chapter a treatment of the Dirichlet problem for sets in the plane is presented. This topic will be continued in Chapter 21 when harmonic measure and logarithmic capacity are introduced and applied. Some material from Chapter 10 must be restated in the more general setting needed for the more extensive study of harmonic functions. In Chapter 10 all functions considered were continuous; here measure theory will be used to broaden the class of functions. The attitude taken will be that usually results from Chapter 10 will be restated in the more inclusive context, but proofs will be furnished only if there is a significant difference between the proof needed at present and the one given for continuous functions.
Publication Year: 1995
Publication Date: 1995-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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