Abstract
A representation theorem is given for ap-harmonic function φ(1<p<∞) in the plane, near a zeroz o of grad φ. The proof uses “stream functions” and the hodograph transformation. The stream function of ap-harmonic function isp′-harmonic, where \(\frac{1}{p} + \frac{1}{{p'}} = 1\). In principle, all properties of φ nearz o can be found from the representation. Some consequences are derived here, e.g. the optimal Hölder continuity of grad φ.
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Aronsson, G. Representation of ap-harmonic function near a critical point in the plane. Manuscripta Math 66, 73–95 (1990). https://doi.org/10.1007/BF02568483
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DOI: https://doi.org/10.1007/BF02568483