Note on a remarkable superposition for a nonlinear equation

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.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2008-01, Vol.136 (1), p.133-140
Main Authors: Lindqvist, Peter, Manfredi, Juan J.
Format: Article
Language:English
Subjects:
College mathematics
Exact sciences and technology
General mathematics
General, history and biography
Mathematical functions
Mathematical theorems
Mathematics
Sciences and techniques of general use
Superharmonics
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-07-09142-3