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Estimates for p-harmonic functions vanishing on a flat
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 74, no 18, 6852-6860 p.Article in journal (Refereed) Published
Abstract [en]

We study p-harmonic functions in a domain ΩCRn near an m-dimensional plane (an m-flat) Λm, where 0≤mn−1. In particular, let u be a positive p-harmonic function, with n<p, vanishing on a portion of Λm, and suppose that β=(pn+m)/(p−1), with β=1 if p=. We prove, using certain barrier functions, that 

 u ≈ d (x.Λm)8   near Λm.

The lower bound holds also in the range nm<p. Moreover, uC0,β near Λm and β is the optimal Hölder exponent of u.

Place, publisher, year, edition, pages
2011. Vol. 74, no 18, 6852-6860 p.
Keyword [en]
Low dimension, Flat, Plane, Boundary Harnack inequality, p-Laplace, Infinity Laplace equation
National Category
Mathematical Analysis
Research subject
Mathematical Statistics; Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-47923DOI: 10.1016/j.na.2011.06.041ISI: 000295714200002OAI: oai:DiVA.org:umu-47923DiVA: diva2:445355
Note

Correction: Niklas L.P. Lundström, Corrigendum to “Estimates for p-harmonic functions vanishing on a flat” [Nonlinear Anal. 74(18) (2011) 6852–6860], Nonlinear Analysis: Theory, Methods & Applications, Volume 129, December 2015, Pages 371-372, ISSN 0362-546X, http://dx.doi.org/10.1016/j.na.2015.08.010

Available from: 2011-10-03 Created: 2011-10-03 Last updated: 2017-10-12
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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