Note on a remarkable superposition for a nonlinear equation
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- by Peter Lindqvist and Juan J. Manfredi PDF
- Proc. Amer. Math. Soc. 136 (2008), 133-140 Request permission
Abstract:
We give a simple proof of—and extend—a superposition principle for the equation $\mbox {div}(|\nabla u|^{p-2}\nabla u)\leq 0$, discovered by Crandall and Zhang. An integral representation comes as a byproduct. It follows that a class of Riesz potentials is $p$-superharmonic.References
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Additional Information
- Peter Lindqvist
- Affiliation: Department of Mathematics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
- MR Author ID: 114355
- Email: lindqvist@math.ntnu.no
- Juan J. Manfredi
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 205679
- Email: manfredi@pitt.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 133-140
- MSC (2000): Primary 35J60, 31C45
- DOI: https://doi.org/10.1090/S0002-9939-07-09142-3
- MathSciNet review: 2350398