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A Remark on the Kelvin Transform for a Quasilinear Equation

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arxiv 1606.02563 v1 pith:JE36DDPO submitted 2016-06-08 math.AP

Peter Lindqvist This is my paper · ORCID
classification math.AP
keywords kelvintransformexponentcasecorrectscounterpartdimensionequal
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The p-harmonic functions are preserved under reflections in spheres only if the exponent p > 1 is equal to the dimension of the underlying Euclidean space. In the linear case p = 2 the Kelvin transform corrects this lack of invariance. We shall show that the Kelvin transform has no reasonable counterpart for general values of the exponent p.

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  1. Critical $p$-Laplace equations with monotone coefficients: Liouville classification and a Schoen-type Harnack inequality

    math.AP 2026-08 accept novelty 8.0 of 10

    Positive entire solutions of the critical p-Laplace equation with monotone coefficient h are always explicit Talenti bubbles, and a scale-invariant Harnack inequality holds.

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