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Note on a remarkable superposition for a nonlinear equation
Author(s):
Peter
Lindqvist;
Juan
J.
Manfredi
Journal:
Proc. Amer. Math. Soc.
136
(2008),
133-140.
MSC (2000):
Primary 35J60, 31C45
Posted:
October 12, 2007
MathSciNet review:
2350398
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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.
References:
-
- [CZ]
- M. CRANDALL & J. ZHANG, Another way to say harmonic, Transactions of the American Mathematical Society 355, 2002, pp. 241-263. MR 1928087 (2003k:35062)
- [JLM]
- P. JUUTINEN, P. LINDQVIST & J. MANFREDI, On the equivalence of viscosity solutions and weak solutions for a quasilinear equation, SIAM Journal on Mathematical Analysis 33, 2001, pp. 699-717. MR 1871417 (2002m:35051)
- [KM]
- T. KILPELÄINEN & J. MALÝ, Degenerate elliptic equations with measure data and nonlinear potentials, Annali della Scuola Normale Superiore di Pisa, Cl. Sci. 4 19, 1992, pp. 591-613. MR 1205885 (94c:35091)
- [L]
- P. LINDQVIST, On the definition and properties of
 -superharmonic functions, Journal für die Reine und Angewandte Mathematik 365, 1986, pp. 67-79. MR 826152 (87e:31011) - [P]
- N. du PLESSIS, An Introduction to Potential Theory, Oliver & Boyd, Edinburgh, 1970. MR 0435422 (55:8382)
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MSC (2000):
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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:
10.1090/S0002-9939-07-09142-3
PII:
S 0002-9939(07)09142-3
Received by editor(s):
September 18, 2006
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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