A Remark on the Kelvin Transform for a Quasilinear Equation
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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