A regularity classification of boundary points for p-harmonic functions and quasiminimizers
2008 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 338, no 1, 39-47 p.Article in journal (Refereed) Published
In this paper it is shown that irregular boundary points for p-harmonic functions as well as for quasiminimizers can be divided into semiregular and strongly irregular points with vastly different boundary behaviour. This division is emphasized by a large number of characterizations of semiregular points. The results hold in complete metric spaces equipped with a doubling measure supporting a Poincaré inequality. They also apply to Cheeger p-harmonic functions and in the Euclidean setting to -harmonic functions, with the usual assumptions on .
Place, publisher, year, edition, pages
2008. Vol. 338, no 1, 39-47 p.
A-harmonic; Dirichlet problem; Doubling measure; Irregular point; Metric space; Nonlinear; p-Harmonic; Poincaré inequality; Quasiharmonic; Quasiminimizer; Semiregular; Strongly irregular
IdentifiersURN: urn:nbn:se:liu:diva-18175DOI: 10.1016/j.jmaa.2007.04.068OAI: oai:DiVA.org:liu-18175DiVA: diva2:216498
Anders Björn, A regularity classification of boundary points for p-harmonic functions and quasiminimizers, 2008, Journal of Mathematical Analysis and Applications, (338), 1, 39-47.
Copyright: Elsevier Science B.V., Amsterdam