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A weak Kellogg property for quasiminimizers
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0002-9677-8321
2006 (English)In: Commentarii Mathematici Helvetici, ISSN 0010-2571, Vol. 81, no 4, 809-825 p.Article in journal (Refereed) Published
Abstract [en]

The Kellogg property says that the set of irregular boundary points has capacity zero, i.e. given a bounded open set Ω there is a set ⊂ ∂Ω with capacity zero such that for all p-harmonic functions u in Ω with continuous boundary values in Sobolev sense, u attains its boundary values at all boundary points in ∂Ω\ E. In this paper, we show a weak Kellogg property for quasiminimizers: a quasiminimizer with continuous boundary values in Sobolev sense takes its boundary values at quasievery boundary point. The exceptional set may however depend on the quasiminimizer. To obtain this result we use the potential theory of quasisuperminimizers and prove a weak Kellogg property for quasisuperminimizers. This is done in complete doubling metric spaces supporting a Poincaré inequality. © Swiss Mathematical Society.

Place, publisher, year, edition, pages
2006. Vol. 81, no 4, 809-825 p.
National Category
URN: urn:nbn:se:liu:diva-30106Local ID: 15575OAI: diva2:250927
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2013-12-17

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