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


Authors: Peter Lindqvist and Juan Manfredi
Journal: Proc. Amer. Math. Soc. 144 (2016), 143-149
MSC (2010): Primary 35J92, 35J62
DOI: https://doi.org/10.1090/proc/12675
Published electronically: May 28, 2015
MathSciNet review: 3415584
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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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Additional Information

Peter Lindqvist
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway

Juan Manfredi
Affiliation: Office of the Provost, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

DOI: https://doi.org/10.1090/proc/12675
Received by editor(s): November 2, 2014
Received by editor(s) in revised form: November 18, 2014
Published electronically: May 28, 2015
Dedicated: To the memory of our friend Albert Baernstein II
Communicated by: Jeremy T. Tyson
Article copyright: © Copyright 2015 American Mathematical Society

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