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Construction of singular solutions to the p-harmonic equation and its limit equation for p=∞
Luleå tekniska universitet.
1986 (engelsk)Inngår i: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 56, nr 2, s. 135-158Artikkel i tidsskrift (Fagfellevurdert) 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).

sted, utgiver, år, opplag, sider
1986. Vol. 56, nr 2, s. 135-158
HSV kategori
Forskningsprogram
Matematik
Identifikatorer
URN: urn:nbn:se:ltu:diva-6538DOI: 10.1007/BF01172152ISI: A1986D514500002Scopus ID: 2-s2.0-0009333821Lokal ID: 4c3f1a40-b4f6-11db-bf94-000ea68e967bOAI: oai:DiVA.org:ltu-6538DiVA, id: diva2:979424
Merknad
Godkänd; 1986; 20070205 (evan)Tilgjengelig fra: 2016-09-29 Laget: 2016-09-29 Sist oppdatert: 2018-07-10bibliografisk kontrollert

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