Remarks on the maximum principle for the \infty-Laplacian
Keywords:
Maximum Principle, Convex Hull Property, \infty-Laplacian, Vector-valued Calculus of Variations in L^\inftyAbstract
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 \infty-Laplacian. The first is the tangential part of the \infty-Laplace system and the second is the scalar \infty-Laplace 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.Downloads
Published
Issue
Section
License
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
