L variational problems for maps and the Aronsson PDE system

Journal of Differential Equations - Tập 253 - Trang 2123-2139 - 2012
Nikolaos I. Katzourakis1
1BCAM (Basque Center for Applied Mathematics), Mazarredo 14, 48009 Bilbao, Spain

Tài liệu tham khảo

Armstrong, 2011, Convexity criteria and uniqueness of absolutely minimizing functions, Arch. Ration. Mech. Anal., 200, 405, 10.1007/s00205-010-0348-0 Aronsson, 1965, Minimization problems for the functional supxF(x,f(x),f′(x)), Ark. Mat., 6, 33, 10.1007/BF02591326 Aronsson, 1966, Minimization problems for the functional supxF(x,f(x),f′(x)) II, Ark. Mat., 6, 409, 10.1007/BF02590964 Aronsson, 1967, Extension of functions satisfying Lipschitz conditions, Ark. Mat., 6, 551, 10.1007/BF02591928 Aronsson, 1968, On the partial differential equation ux2uxx+2uxuyuxy+uy2uyy=0, Ark. Mat., 7, 395, 10.1007/BF02590989 Aronsson, 1969, Minimization problems for the functional supxF(x,f(x),f′(x)) III, Ark. Mat., 509, 10.1007/BF02590888 Aronsson, 1984, On certain singular solutions of the partial differential equation ux2uxx+2uxuyuxy+uy2uyy=0, Manuscripta Math., 47, 133, 10.1007/BF01174590 Aronsson, 1986, Construction of singular solutions to the p-harmonic equation and its limit equation for p=∞, Manuscripta Math., 56, 135, 10.1007/BF01172152 Barron, 2008, The infinity Laplacian, Aronssonʼs equation and their generalizations, Trans. Amer. Math. Soc., 360, 10.1090/S0002-9947-07-04338-3 Barron, 2001, The Euler equation and absolute minimizers of L∞ functionals, Arch. Ration. Mech. Anal., 157, 255, 10.1007/PL00004239 Barron, 2001, Lower semicontinuity of L∞ functionals, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18, 495, 10.1016/s0294-1449(01)00070-1 Bieske, 2005, The Aronsson–Euler equation for absolutely minimizing extensions with respect to Carnot–Carathéodory metrics, Trans. Amer. Math. Soc., 357, 795, 10.1090/S0002-9947-04-03601-3 Crandall, 2005, A visit with the ∞-Laplacian, vol. 1927 Crandall, 2001, Optimal Lipschitz extensions and the infinity Laplacian, Calc. Var. Partial Differential Equations, 13, 123, 10.1007/s005260000065 Capogna, 2012, An Aronsson type approach to extremal quasiconformal mappings, J. Differential Equations, 253, 851, 10.1016/j.jde.2012.04.015 Danskin, 1966, The theory of min-max with application, SIAM J. Appl. Math., 14, 641, 10.1137/0114053 Crandall, 2009, Derivation of the Aronsson equation for C1 Hamiltonians, Trans. Amer. Math. Soc., 361, 103, 10.1090/S0002-9947-08-04651-5 Juutinen, 2007, Hamilton–Jacobi flows and characterization of solutions of Aronsson equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 6, 1 Jensen, 1993, Uniqueness of Lipschitz extensions minimizing the sup-norm of the gradient, Arch. Ration. Mech. Anal., 123, 51, 10.1007/BF00386368 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 Y.L. Ou, T. Troutman, F. Wilhelm, Infinity-harmonic maps and morphisms, preprint, 2011. Peres, 2009, Tug-of-war and the infinity Laplacian, J. Amer. Math. Soc., 22, 167, 10.1090/S0894-0347-08-00606-1 Simon, 1983, Lectures on Geometric Measure Theory, vol. 3 Sheffield, 2012, Vector valued optimal Lipschitz extensions, Comm. Pure Appl. Math., 65, 128, 10.1002/cpa.20391 Wang, 2009, Classifications of some special infinity-harmonic maps, Balkan J. Geom. Appl., 14, 120 Yu, 2006, L∞ variational problems and Aronsson equations, Arch. Ration. Mech. Anal., 182, 153, 10.1007/s00205-006-0424-7