Abstract
In this chapter harmonic functions will be studied and the Dirichlet Problem will be solved. The Dirichlet Problem consists in determining all regions G such that for any continuous function f: əG → ℝ there is a continuous function u:G−→ℝ such that u(z) = f(z) for z in əG and u is harmonic in G. Alternately, we are asked to determine all regions G such that Laplace’s Equation is solvable with arbitrary boundary values.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1973 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Conway, J.B. (1973). Harmonic Functions. In: Functions of One Complex Variable. Graduate Texts in Mathematics, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-9972-2_10
Download citation
DOI: https://doi.org/10.1007/978-1-4615-9972-2_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90062-9
Online ISBN: 978-1-4615-9972-2
eBook Packages: Springer Book Archive