On the asymptotic mean value property for planar $p$-harmonic functions
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- by Ángel Arroyo and José G. Llorente PDF
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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 a certain range of $p$’s.References
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Additional Information
- Ángel Arroyo
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Spain
- Email: arroyo@mat.uab.cat
- José G. Llorente
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bella- terra, Barcelona, Spain
- MR Author ID: 327617
- Email: jgllorente@mat.uab.cat
- Received by editor(s): September 4, 2015
- Received by editor(s) in revised form: October 29, 2015
- Published electronically: February 17, 2016
- Additional Notes: The authors were partially supported by grants MTM2011-24606, MTM2014-51824-P and 2014 SGR 75.
- Communicated by: Joachim Krieger
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 3859-3868
- MSC (2010): Primary 31C05, 35J92, 35J62
- DOI: https://doi.org/10.1090/proc/13026
- MathSciNet review: 3513544