Remarks on the validity on the maximum principle for the ∞-Laplacian

Katzourakis, N. and Manfredi, J. (2016) Remarks on the validity on the maximum principle for the ∞-Laplacian. Le Matematiche, 71. pp. 63-74. ISSN 2037-5298 doi: 10.4418/2016.71.1.5

Abstract/Summary

In this note we give three counter-examples which show that the Maximum Principle generally fails for classical solutions of a system and a single equation related to the ∞-Laplacian. The first is the tangential part of the ∞-Laplacian system and the second is the scalar ∞-Laplacian equation perturbed by a linear gradient term. The interpretations of the Maximum Principle for the system are that of the Convex Hull Property and also of the Maximum Principle of the modulus of the solution.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/47117
Identification Number/DOI	10.4418/2016.71.1.5
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Dipartimento di Matematica e Informatica of the University of Catania
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