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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mean value property for $ p$-harmonic functions


Authors: Tiziana Giorgi and Robert Smits
Journal: Proc. Amer. Math. Soc. 140 (2012), 2453-2463
MSC (2010): Primary 35J92, 35D40, 35J60, 35J70
Published electronically: November 21, 2011
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Abstract: We derive a mean value property for $ p$-harmonic functions in two dimensions, $ 1<p<\infty $, which holds asymptotically in the viscosity sense. The formula coincides with the classical mean value property for harmonic functions, when $ p=2$, and is a consequence of a representation for the Game $ p$-Laplacian obtained via $ p$-averaging.


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Additional Information

Tiziana Giorgi
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001
Email: tgiorgi@nmsu.edu

Robert Smits
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001
Email: rsmits@nmsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11181-X
PII: S 0002-9939(2011)11181-X
Received by editor(s): November 1, 2010
Received by editor(s) in revised form: February 26, 2011
Published electronically: November 21, 2011
Additional Notes: Funding for the first author was provided by National Science Foundation Grant #DMS-0604843
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.