Harmonic Functions and Integral Functions

Hemant Kumar Pathak ()
Additional contact information
Hemant Kumar Pathak: Pt. Ravishankar Shukla University, School of Studies in Mathematics

Chapter Chapter 11 in Complex Analysis and Applications, 2019, pp 753-805 from Springer

Abstract: Abstract In this chapter, we shall study harmonic function, Harnack’s inequalityHarnack’s inequality, and the Dirichlet problemDirichlet problem will be solved. The Dirichlet problem consists in determining all regions G such that for any continuous function $$f: \partial G \rightarrow \mathbb {R}$$ there is a continuous function $$ u :\overline{G} \rightarrow \mathbb {R}$$ such that $$u(z) = f(z)$$ for $$z \in \partial G$$ and u is harmonic in G. Alternatively, the Dirichlet problem consists in determining all regions G such that Laplace’s equation isLaplace’s Equation solvable with arbitrary boundary values.

Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-9734-9_11

Ordering information: This item can be ordered from
http://www.springer.com/9789811397349

DOI: 10.1007/978-981-13-9734-9_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().