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Mean value property for  -harmonic functions
Authors:
Tiziana Giorgi and Robert Smits
Journal:
Proc. Amer. Math. Soc. 140 (2012), 2453-2463
MSC (2010):
Primary 35J92, 35D40, 35J60, 35J70
Posted:
November 21, 2011
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Additional Information
Abstract: We derive a mean value property for  -harmonic functions in two dimensions,  , which holds asymptotically in the viscosity sense. The formula coincides with the classical mean value property for harmonic functions, when  , and is a consequence of a representation for the Game  -Laplacian obtained via  -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
Posted:
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 after
28 years from publication.
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