Explicit 2D ∞-harmonic maps whose interfaces have junctions and corners

Comptes Rendus Mathematique - Tập 351 - Trang 677-680 - 2013
Nicholas Katzourakis1,2
1BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009, Bilbao, Spain
2Department of Mathematics and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, Berkshire, UK

Tài liệu tham khảo

Aronsson, 1968, On the partial differential equation ux2uxx+2uxuyuxy+uy2uyy=0, Ark. Mat., 7, 395, 10.1007/BF02590989

Aronsson, 1984, On certain singular solutions of the partial differential equation ux2uxx+2uxuyuxy+uy2uyy=0, Manuscr. Math., 47, 133, 10.1007/BF01174590

Capogna, 2012, An Aronsson-type approach to extremal quasiconformal mappings, J. Differ. Equ., 253, 851, 10.1016/j.jde.2012.04.015

Crandall, 2005, A visit with the ∞-Laplacian, vol. 1927

Crandall, 1992, Userʼs guide to viscosity solutions of 2nd-order partial differential equations, Bull. Am. Math. Soc., 27, 1, 10.1090/S0273-0979-1992-00266-5

Katzourakis, 2011, Explicit singular viscosity solutions of the Aronsson equation, C. R. Acad. Sci. Paris, Ser. I, 349, 1173, 10.1016/j.crma.2011.10.010

Katzourakis, 2013, The subelliptic ∞-Laplace system on Carnot–Carathéodory spaces, Adv. Nonlinear Anal., 2, 213, 10.1515/anona-2013-0004

Sheffield, 2012, Vector valued optimal Lipschitz extensions, Commun. Pure Appl. Math., 65, 128, 10.1002/cpa.20391