Year: 2012
Type: article
Abstract: We identify the Variational Principle governing inifinity-Harmonic maps, that is solutions to the Infinity-Laplacian. The system was first derived in the limit of the p-Laplacian as p->inifinity in [K2] and is recently studied in [K3]. Here we show that it is the "Euler-Lagrange PDE" of vector-valued Calculus of Variations in L-inifinity for the L-inifinity norm of the gradient. We introduce the notion of inifinity-Minimal Maps, whch are Rank-One Absolute Minimals of with inifinity-Minimal Area" of the range submanifold and prove they solve the inifinity-laplacian. The converse is true for immersions. We also establish a maximum principle for |Du| for solutions. We further characterize minimal surfaces of 3-space as those locally parameterizable by isothermal immersions with inifinity-minimal area and show that isothermal inifinity-Harmonic maps are rigid.
Source: CentAUR (University of Reading)
Author: Katzourakis, Nikolaos I.
Institution: Basque Center for Applied Mathematics
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1880210604