Abstract
A representation theorem is given for certainp-harmonic functions (1<p<∞) in the plane, near a corner of the domain of definition. The proof uses “stream functions” and the hodograph transformation. The stream function of ap-harmonic function isp′-harmonic, where 1/p+1/p′=1. Solutions of the formr k f(ø) (polar coord.) are crucial for the representation.
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Aronsson, G. On certainp-harmonic functions in the plane. Manuscripta Math 61, 79–101 (1988). https://doi.org/10.1007/BF01153584
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DOI: https://doi.org/10.1007/BF01153584