Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

On the asymptotic mean value property for planar $ p$-harmonic functions


Authors: Ángel Arroyo and José G. Llorente
Journal: Proc. Amer. Math. Soc. 144 (2016), 3859-3868
MSC (2010): Primary 31C05, 35J92, 35J62
Published electronically: February 17, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 31C05, 35J92, 35J62

Retrieve articles in all journals with MSC (2010): 31C05, 35J92, 35J62


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
Email: jgllorente@mat.uab.cat

DOI: https://doi.org/10.1090/proc/13026
Keywords: Mean value property, $p$-harmonic function
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
Article copyright: © Copyright 2016 American Mathematical Society