On the asymptotic mean value property for planar p-harmonic functions
Angel Arroyo, Jos\'e G. Llorente
TL;DR
This paper proves that planar p-harmonic functions satisfy a nonlinear asymptotic mean value property for p>1, extending earlier results to a broader range of p values.
Contribution
It establishes a generalized asymptotic mean value property for p-harmonic functions in the plane, broadening the scope of previous findings.
Findings
p-harmonic functions satisfy a nonlinear asymptotic mean value property
Extension of previous results to a wider range of p values
Provides theoretical foundation for further analysis of p-harmonic functions
Abstract
We show that p-harmonic functions in the plane satisfy a nonlinear asymptotic mean value property for p>1. This extends previous results of Manfredi and Lindqvist for certain range of p's.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Numerical methods in inverse problems