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 | References | Similar Articles | Additional Information

Abstract: We give a simple proof of--and extend--a superposition principle for the equation div, discovered by Crandall and Zhang. An integral representation comes as a byproduct. It follows that a class of Riesz potentials is -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

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.