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Construction of singular solutions to the p-harmonic equation and its limit equation for p=∞
Luleå tekniska universitet.
1986 (English)In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 56, no 2, p. 135-158Article in journal (Refereed) Published
Abstract [en]

Here, all solutions of the form u=rkf(φ) to the p-harmonic equation, div(|∇u|p-2∇u)=0, (p>2) in the plane are determined. One main result is a representation formula for such solutions. Further, solutions with an isolated singularity at the origin are constructed (Theorem 1). Graphical illustrations are given at the end of the paper. Finally, all solutions u=rkf(φ) of the limit equation for p=∞, ux2uxx+2uxuyuxy+uy2uyy=2, are constructed, some of which have a "strong" singularity at the origin (Theorem 2).

Place, publisher, year, edition, pages
1986. Vol. 56, no 2, p. 135-158
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-6538DOI: 10.1007/BF01172152Local ID: 4c3f1a40-b4f6-11db-bf94-000ea68e967bOAI: oai:DiVA.org:ltu-6538DiVA: diva2:979424
Note
Godkänd; 1986; 20070205 (evan)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-21Bibliographically approved

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