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

 

Note on a remarkable superposition for a nonlinear equation


Authors: Peter Lindqvist and Juan J. Manfredi
Journal: Proc. Amer. Math. Soc. 136 (2008), 133-140
MSC (2000): Primary 35J60, 31C45
Published electronically: October 12, 2007
MathSciNet review: 2350398
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Abstract: We give a simple proof of--and extend--a superposition principle for the equation div$ (\vert\nabla u\vert^{p-2}\nabla u)\leq 0$, discovered by Crandall and Zhang. An integral representation comes as a byproduct. It follows that a class of Riesz potentials is $ p$-superharmonic.


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Additional Information

Peter Lindqvist
Affiliation: Department of Mathematics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Email: lindqvist@math.ntnu.no

Juan J. Manfredi
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: manfredi@pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-09142-3
PII: S 0002-9939(07)09142-3
Received by editor(s): September 18, 2006
Published electronically: October 12, 2007
Additional Notes: This paper was written while the first author was visiting the University of Pittsburgh. He wishes to acknowledge the hospitality and the stimulating working atmosphere at the Department of Mathematics. The second author was partially supported by NSF award DMS-0500983.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.