2013/03/01 by Nicholas Katzourakis, Katzourakis, Nicholas
Mathematics · Physics and Astronomy · #35J62 #53C24 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 35J47 #Secondary 49J99 #math.AP #msc:35J47 #msc:35J62 #msc:49J99 #msc:53C24
paper · pdf · doi:10.48550/arxiv.1303.0240
16 pages, 2 figures, to appear in Advances in Nonlinear Analysis
openalex publication_date 2013/03/01 · arxiv created 2013/04/11 · arxiv updated 2013/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a Carnot-Carathéodory space \Om \sub \Rn with associated vector fields X=\X1,...,Xm\, we derive the subelliptic ∞-Laplace system for mappings u : \Om \larrow \RN, which reads \DeX_∞ u := (Xu \ot Xu + ‖Xu‖2 [Xu]^\bot \ot I ) : XX u = 0 in the limit of the subelliptic p-Laplacian as p\ri ∞. Here Xu is the horizontal gradient and [Xu]^\bot is the projection on its nullspace. Next, we identify the Variational Principle characterizing \eqref1, which is the "Euler-Lagrange PDE" of the supremal functional E_∞(u,\Om) := ‖Xu‖L^∞(\Om) for an appropriately defined notion of Horizontally ∞-Minimal Mappings. We also establish a maximum principle for ‖Xu‖ for solutions to \eqref1. These results extend previous work of the author \citeK1, K2 on vector-valued Calculus of Variations in L^∞ from the Euclidean to the subelliptic setting.