Harnack Inequalities: An Introduction

Harnack Inequalities: An Introduction

The aim of this article is to give an introduction to certain inequalities named after Carl Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions in the plane and much later became an important tool in the general theory of harmonic functions and partial differen...

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Main Author: Moritz Kassmann
Format: Article
Language:English
Published: SpringerOpen 2007-01-01
Series:Boundary Value Problems
Online Access:http://dx.doi.org/10.1155/2007/81415
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spelling doaj-e234e65e94df47428cd6d5dbd859aec92020-11-24T21:11:29ZengSpringerOpenBoundary Value Problems1687-27621687-27702007-01-01200710.1155/2007/81415Harnack Inequalities: An IntroductionMoritz KassmannThe aim of this article is to give an introduction to certain inequalities named after Carl Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions in the plane and much later became an important tool in the general theory of harmonic functions and partial differential equations. We restrict ourselves mainly to the analytic perspective but comment on the geometric and probabilistic significance of Harnack inequalities. Our focus is on classical results rather than latest developments. We give many references to this topic but emphasize that neither the mathematical story of Harnack inequalities nor the list of references given here is complete.http://dx.doi.org/10.1155/2007/81415
collection DOAJ
language English
format Article
sources DOAJ
author Moritz Kassmann
spellingShingle Moritz Kassmann
Harnack Inequalities: An Introduction
Boundary Value Problems
author_facet Moritz Kassmann
author_sort Moritz Kassmann
title Harnack Inequalities: An Introduction
title_short Harnack Inequalities: An Introduction
title_full Harnack Inequalities: An Introduction
title_fullStr Harnack Inequalities: An Introduction
title_full_unstemmed Harnack Inequalities: An Introduction
title_sort harnack inequalities: an introduction
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2762
1687-2770
publishDate 2007-01-01
description The aim of this article is to give an introduction to certain inequalities named after Carl Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions in the plane and much later became an important tool in the general theory of harmonic functions and partial differential equations. We restrict ourselves mainly to the analytic perspective but comment on the geometric and probabilistic significance of Harnack inequalities. Our focus is on classical results rather than latest developments. We give many references to this topic but emphasize that neither the mathematical story of Harnack inequalities nor the list of references given here is complete.
url http://dx.doi.org/10.1155/2007/81415
work_keys_str_mv AT moritzkassmann harnackinequalitiesanintroduction
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