Change search
ReferencesLink to record
Permanent link

Direct link
Boundary behavior and the Martin boundary problem for p harmonic functions in Lipschitz domains
Umeå University, Faculty of Science and Technology, Department of mathematics.
2010 (English)In: Annals of Mathematics, ISSN 0003-486X, E-ISSN 1939-8980, Vol. 172, no 3, 1907-1948 p.Article in journal (Refereed) Published
Abstract [en]

In a previous article, we proved a boundary Harnack inequality for the ratio of two positive p harmonic functions, vanishing on a portion of the boundary of a Lipschitz domain. In the current paper we continue our study by showing that this ratio is Holder continuous up to the boundary. We also consider the Martin boundary of certain domains and the corresponding question of when a minimal positive p harmonic function (with respect to a given boundary point w) is unique up to constant multiples. In particular we show that the Martin boundary can be identified with the topological boundary in domains that are convex or C(1). Minimal positive p harmonic functions relative to a boundary point w in a Lipschitz domain are shown to be unique, up to constant multiples, provided the boundary is sufficiently flat at w.

Place, publisher, year, edition, pages
Princeton University, Department of Mathematics , 2010. Vol. 172, no 3, 1907-1948 p.
National Category
URN: urn:nbn:se:umu:diva-109572DOI: 10.4007/annals.2010.172.1907ISI: 000282652000011OAI: diva2:857989
Available from: 2015-09-30 Created: 2015-09-30 Last updated: 2015-09-30Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Nyström, Kaj
By organisation
Department of mathematics
In the same journal
Annals of Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 7 hits
ReferencesLink to record
Permanent link

Direct link