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Boundary estimates for solutions to operators of p-Laplace type with lower order terms
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.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2011 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 250, no 1, 264-291 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the boundary behavior of solutions to equations of the form∇⋅A(x,∇u)+B(x,∇u)=0, in a domain ΩRn, assuming that Ω is a δ-Reifenberg flat domain for δ sufficiently small. The function A is assumed to be of p-Laplace character. Concerning B, we assume that |∇ηB(x,η)|⩽c|η|p−2, |B(x,η)|⩽c|η|p−1, for some constant c, and that B(x,η)=|η|p−1B(x,η/|η|), whenever xRn, ηRn∖{0}. In particular, we generalize the results proved in J. Lewis et al. (2008) [12] concerning the equation ∇⋅A(x,∇u)=0, to equations including lower order terms.

Place, publisher, year, edition, pages
2011. Vol. 250, no 1, 264-291 p.
Keyword [en]
Boundary Harnack inequality, p-harmonic function, A-harmonic function, (A, B)-harmonic function, Variable coefficients, Operators with lower order terms, Reifenberg flat domain, Martin boundary
National Category
Mathematics Probability Theory and Statistics
Research subject
Mathematical Statistics; Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-40224DOI: 10.1016/j.jde.2010.09.011ISI: 000284919600013OAI: oai:DiVA.org:umu-40224DiVA: diva2:398451
Available from: 2011-02-17 Created: 2011-02-17 Last updated: 2017-12-11Bibliographically 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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Avelin, BennyLundström, Niklas L.P.Nyström, Kaj
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