On the mean value property for the 𝑝-Laplace equation in the plane

Lindqvist, Peter; Manfredi, Juan

doi:10.1090/proc/12675

On the mean value property for the $p$-Laplace equation in the plane
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by Peter Lindqvist and Juan Manfredi

Proc. Amer. Math. Soc. 144 (2016), 143-149

DOI: https://doi.org/10.1090/proc/12675

Published electronically: May 28, 2015

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Abstract:

We study the $p$-Laplace equation in the plane and prove that the mean value property holds directly for the solutions themselves for $1<p<9.525...$. This removes the need to interpret the formula in the viscosity sense via test functions. The method is based on the hodograph representation.

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