@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}, pages = {659--678}, publisher = {Elsevier}, volume = {25}, number = {4}, year = {2008}, doi = {10.1016/j.anihpc.2007.03.003}, mrnumber = {2436787}, zbl = {1179.35124}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.003/} }
TY - JOUR AU - Wang, Changyou AU - Yu, Yifeng TI - ${C}^{1}$-regularity of the Aronsson equation in ${R}^{2}$ JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 659 EP - 678 VL - 25 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.003/ DO - 10.1016/j.anihpc.2007.03.003 LA - en ID - AIHPC_2008__25_4_659_0 ER -
%0 Journal Article %A Wang, Changyou %A Yu, Yifeng %T ${C}^{1}$-regularity of the Aronsson equation in ${R}^{2}$ %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 659-678 %V 25 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.003/ %R 10.1016/j.anihpc.2007.03.003 %G en %F 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) no. 4, pp. 659-678. doi : 10.1016/j.anihpc.2007.03.003. https://www.numdam.org/articles/10.1016/j.anihpc.2007.03.003/
[1] Minimization problems for the functional sup
[2] Minimization problems for the functional sup
[3] Minimization problems for the functional sup
[4] Extension of functions satisfying Lipschitz conditions, Ark. Mat. 6 (1967) 551-561. | MR | Zbl
,
[5] On the partial differential equation
[6] On certain singular solutions of the partial differential equation
[7] A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc. (N.S.) 41 (4) (2004) 439-505, (electronic). | MR | Zbl
, , ,
[8] Viscosity solutions and analysis in
[9] Minimizing the
[10] Lower semicontinuity of
[11] The Euler equation and absolute minimizers of
[12] An efficient derivation of the Aronsson equation, Arch. Ration. Mech. Anal. 167 (4) (2003) 271-279. | MR | Zbl
,[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 | Zbl
[16] Optimal Lipschitz extensions and the infinity Laplacian, Calc. Var. Partial Differential Equations 13 (2) (2001) 123-139. | MR | Zbl
, , ,[17] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1) (1992) 1-67. | MR | Zbl
, , ,[18] 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
, , ,[19] Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient, Arch. Ration. Mech. Anal. 123 (1) (1993) 51-74. | MR | Zbl
,[20] Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952) 25-53. | MR | Zbl
,
[21]
[22]
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