C 1 -regularity of the Aronsson equation in R 2
Wang, Changyou ; Yu, Yifeng
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 659-678 / Harvested from Numdam
@article{AIHPC_2008__25_4_659_0,
     author = {Wang, Changyou and Yu, Yifeng},
     title = {${C}^{1}$-regularity of the Aronsson equation in ${R}^{2}$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {659-678},
     doi = {10.1016/j.anihpc.2007.03.003},
     mrnumber = {2436787},
     zbl = {1179.35124},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_4_659_0}
}
Wang, Changyou; Yu, Yifeng. ${C}^{1}$-regularity of the Aronsson equation in ${R}^{2}$. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 659-678. doi : 10.1016/j.anihpc.2007.03.003. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_4_659_0/

[1] Aronsson G., Minimization problems for the functional sup xF(x,f(x),f(x, Ark. Mat. 6 (1965) 33-53. | MR 196551 | Zbl 0156.12502

[2] Aronsson G., Minimization problems for the functional sup xF(x,f(x),f(x. II, Ark. Mat. 6 (1966) 409-431. | MR 203541 | Zbl 0156.12502

[3] Aronsson G., Minimization problems for the functional sup xF(x,f(x),f(x. III, Ark. Mat. 7 (1969) 509-512. | MR 240690 | Zbl 0181.11902

[4] Aronsson G., Extension of functions satisfying Lipschitz conditions, Ark. Mat. 6 (1967) 551-561. | MR 217665 | Zbl 0158.05001

[5] Aronsson G., On the partial differential equation u x 2 u xx +2u x u y u xy +u y 2 u yy =0, Ark. Mat. 7 (1968) 395-425. | MR 237962 | Zbl 0162.42201

[6] Aronsson G., On certain singular solutions of the partial differential equation u x 2 u xx +2u x u y u xy +u y 2 u yy =0, Manuscripta Math. 47 (1-3) (1984) 133-151. | MR 744316 | Zbl 0551.35018

[7] Aronsson G., Crandall M., Juutinen P., A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc. (N.S.) 41 (4) (2004) 439-505, (electronic). | MR 2083637 | Zbl 1150.35047

[8] Barron N., Viscosity solutions and analysis in L , in: Nonlinear Analysis, Differential Equations and Control, Montreal, QC, 1998, NATO Sci. Ser. C Math. Phys. Sci., vol. 528, Kluwer Acad. Publ., Dordrecht, 1999, pp. 1-60. | MR 1695005 | Zbl 0973.49024

[9] Barron N., Jensen R., Minimizing the L -norm of the gradient with an energy constraint, Comm. Partial Differential Equations 30 (10-12) (2005) 1741-1772. | MR 2182310 | Zbl 1105.35028

[10] Barron N., Jensen R., Wang C.Y., Lower semicontinuity of L functionals, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (4) (2001) 495-517. | Numdam | MR 1841130 | Zbl 1034.49008

[11] Barron N., Jensen R., Wang C.Y., The Euler equation and absolute minimizers of L functionals, Arch. Ration. Mech. Anal. 157 (4) (2001) 255-283. | MR 1831173 | Zbl 0979.49003

[12] Crandall M., An efficient derivation of the Aronsson equation, Arch. Ration. Mech. Anal. 167 (4) (2003) 271-279. | MR 1981858 | Zbl 1090.35067

[13] M. Crandall, The infinity-Laplace equation and the elements of calculus of variations in L-infinity, in: CIME Lecture Notes, in press.

[14] M. Crandall, The continuous gradient flow for the infinity-Laplace equation, Private communication.

[15] M. Crandall, L.C. Evans, A remark on infinity harmonic functions, in: Proceedings of the USA-Chile Workshop on Nonlinear Analysis, Via del Mar-Valparaiso, 2000 (electronic), Electron. J. Differ. Equ. Conf., 6, pp. 123-129. | MR 1804769 | Zbl 0964.35061

[16] Crandall M., Evans C., Gariepy R., Optimal Lipschitz extensions and the infinity Laplacian, Calc. Var. Partial Differential Equations 13 (2) (2001) 123-139. | MR 1861094 | Zbl 0996.49019

[17] Crandall M., Ishii H., Lions P.L., User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1) (1992) 1-67. | MR 1118699 | Zbl 0755.35015

[18] Gariepy R., Wang C.Y., Yu Y., Generalized cone comparison principle for viscosity solutions of the Aronsson equation and absolute minimizers, Comm. Partial Differential Equations 31 (7-9) (2006) 1027-1046. | MR 2254602 | Zbl pre05062565

[19] Jensen R., Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient, Arch. Ration. Mech. Anal. 123 (1) (1993) 51-74. | MR 1218686 | Zbl 0789.35008

[20] Morrey C.B., Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952) 25-53. | MR 54865 | Zbl 0046.10803

[21] Savin O., C 1 -regularity for infinity harmonic functions in dimensions two, Arch. Ration. Mech. Anal. 176 (3) (2005) 351-361. | MR 2185662 | Zbl 1112.35070

[22] Yu Y., L -variational problems and the Aronsson equations, Arch. Ration. Mech. Anal. 182 (1) (2006) 153-180. | MR 2247955 | Zbl 1130.49025