Perron's method for p-harmonious functions

We show that Perron's method produces continuous p-harmonious functions for 1<p<2. Such functions approximate p-harmonic functions and satisfy a functional equation involving a convex combination of the mean and median, generalizing the classical mean-value property of harmonic functions....

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2016; no. 123; pp. 1 - 12
Main Authors David Hartenstine, Matthew Rudd
Format Journal Article
LanguageEnglish
Published Texas State University 16.05.2016
Subjects
Mean-value property
median
p-harmonic functions
p-harmonious functions
p-Laplacian
Perron method
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Summary:We show that Perron's method produces continuous p-harmonious functions for 1<p<2. Such functions approximate p-harmonic functions and satisfy a functional equation involving a convex combination of the mean and median, generalizing the classical mean-value property of harmonic functions. Simple sufficient conditions for the existence of barriers are given. The p=1 situation, in which solutions to the Dirichlet problem may not be unique, is also considered. Finally, the relationship between 1-harmonious functions and functions satisfying a local median value property is discussed.
ISSN:1072-6691