Preliminaries on Harmonic Functions

Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino
Additional contact information
Matteo Dalla Riva: The University of Tulsa, College of Engineering and Natural Science
Massimo Lanza de Cristoforis: Università degli Studi di Padova, Dipartimento di Matematica
Paolo Musolino: Università Ca’ Foscari Venezia, Dipartimento di Scienze Molecolari e Nanosistemi

Chapter Chapter 3 in Singularly Perturbed Boundary Value Problems, 2021, pp 113-121 from Springer

Abstract: Abstract This chapter is devoted to the properties of harmonic functions that we exploit in this book. For most of the proofs we refer to classic monographs and in particular to Evans (Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition, 2010), Folland (Introduction to partial differential equations. Princeton University Press, Princeton, NJ, second edition, 1995), and Gilbarg and Trudinger (Elliptic partial differential equations of second order, volume 224 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition, 1983). We present the Maximum Principle, the Liouville Theorem, the interior inequalities for the derivatives of a harmonic function, Weyl’s Lemma, the Lemma of Hopf-Oleı̆nik, some properties of harmonic functions around isolated singularities, the Kelvin transform, and some properties of harmonic functions at infinity.

Date: 2021
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:978-3-030-76259-9_3

Ordering information: This item can be ordered from
http://www.springer.com/9783030762599

DOI: 10.1007/978-3-030-76259-9_3

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 ().