A Remark on the Kelvin Transform for a Quasilinear Equation

Abstract

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.