Article ; Online: Perron's method for p-harmonious functions
Electronic Journal of Differential Equations, Vol 2016, Iss 123,, Pp 1-
2016 Volume 12
Abstract: 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 ... conditions for the existence of barriers are given. The p=1 situation, in which solutions to the Dirichlet ...
Abstract | 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. |
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Keywords | Mean-value property ; median ; p-harmonic functions ; p-Laplacian ; p-harmonious functions ; Perron method ; Mathematics ; QA1-939 ; Science ; Q |
Language | English |
Publishing date | 2016-05-01T00:00:00Z |
Publisher | Texas State University |
Document type | Article ; Online |
Database | BASE - Bielefeld Academic Search Engine (life sciences selection) |
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