Remarks on the validity on the maximum principle for the ∞-LaplacianKatzourakis, 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
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.4418/2016.71.1.5 Abstract/SummaryIn 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.
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