New explicit solutions to the p-Laplace equation based on isoparametric foliations

被引：1

作者：

Tkachev, Vladimir G. ^{[1
]}

机构：

[1] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2020年 / 70卷

关键词：

Isoparametric polynomials; p-Laplacian; infinity-Laplacian; Biharmonic functions; Minimal submanifold; Focal varieties; HARMONIC FUNCTIONS; MINIMAL HYPERSURFACES; SINGULAR SOLUTIONS; CONSTRUCTION; SYSTEMS; CONES;

D O I：

10.1016/j.difgeo.2020.101629

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In contrast to an infinite family of explicit examples of two-dimensional p-harmonic functions obtained by G. Aronsson in the late 80s, there is very little known about the higher-dimensional case. In this paper, we show how to use isoparametric polynomials to produce diverse examples of p-harmonic and biharmonic functions. Remarkably, for some distinguished values of p and the ambient dimension n this yields first examples of rational and algebraic p-harmonic functions. Moreover, we show that there are no p-harmonic polynomials of the isoparametric type. This supports a negative answer to a question proposed in 1980 by J. Lewis. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：18

共 65 条

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[2]