The subelliptic ∞-Laplace system on Carnot–Carathéodory spaces

Advances in Nonlinear Analysis - Tập 2 Số 2 - Trang 213-233 - 2013
Nicholas Katzourakis1,2
1Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E48009, Bilbao, Spain
2Department of Mathematics and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, Berkshire, UK; and Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E48009, Bilbao, Spain

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Abstract. Given a Carnot–Carathéodory space with associated frame of vector fields , we derive the subelliptic ∞-Laplace system for mappings , which reads in the limit of the subelliptic p-Laplacian as . Here is the horizontal gradient and is the projection on its nullspace. Next, we identify the variational principle characterizing the subelliptic ∞-Laplacian system, which is the “Euler–Lagrange PDE” of the supremal functional for an appropriately defined notion of horizontally ∞-minimal mappings. We also establish a maximum principle for for solutions to the subelliptic ∞-Laplacian system. These results extend previous work of the author [J. Differential Equations 253 (2012), no. 7, 2123–2139; Proc. Amer. Math. Soc., to appear] on vector-valued calculus of variations in L ∞ from the Euclidean to the subelliptic setting.

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Advances in Nonlinear Analysis

Tập 2 Số 2

213-233

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