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The Boundary Harnack Inequality for Solutions to Equations of Aronsson type in the Plane
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Annales Academiae Scientiarum Fennicae Mathematica, ISSN 1239-629X, E-ISSN 1798-2383, Vol. 36, 261-278 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we prove a boundary Harnack inequality for positive functions which vanish continuously on a portion of the boundary of a bounded domain \Omega \subset R2 and which are solutions to a general equation of p-Laplace type, 1 < p < \infty. We also establish the same type of result for solutions to the Aronsson type equation \nabla (F(x,\nabla u)) \cdot F\eta(x,\nabla u) = 0. Concerning \Omega we only assume that \partial\Omega is a quasicircle. In particular, our results generalize the boundary Harnack inequalities in [BL] and [LN2] to operators with variable coefficients.

Place, publisher, year, edition, pages
Academia Scientiarum Fennica , 2011. Vol. 36, 261-278 p.
Keyword [en]
Boundary Harnack inequality, p-Laplace, A-harmonic function, infinity harmonic function, Aronsson type equation, quasicircle
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-40225DOI: 10.5186/aasfm.2011.3616OAI: oai:DiVA.org:umu-40225DiVA: diva2:398453
Available from: 2011-02-17 Created: 2011-02-17 Last updated: 2015-03-16Bibliographically approved
In thesis
1. p-harmonic functions near the boundary
Open this publication in new window or tab >>p-harmonic functions near the boundary
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för matematik och matematisk statistik, 2011. 228 p.
Series
Doctoral thesis / Umeå University, Department of Mathematics, ISSN 1102-8300 ; 50
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:umu:diva-47942 (URN)978-91-7459-287-0 (ISBN)
Public defence
2011-10-28, Mit-huset, MA121, Umeå universitet, Umeå, 10:00
Opponent
Supervisors
Available from: 2011-10-07 Created: 2011-10-04 Last updated: 2011-10-04Bibliographically approved

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Lundström, Niklas L.P.Nyström, Kaj

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