@article{ASNSP_2003_5_2_4_847_0, author = {Balogh, Zolt\'an M. and Rickly, Matthieu}, title = {Regularity of convex functions on Heisenberg groups}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {4}, year = {2003}, pages = {847-868}, zbl = {1121.43007}, mrnumber = {2040646}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_4_847_0} }
Balogh, Zoltán M.; Rickly, Matthieu. Regularity of convex functions on Heisenberg groups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 4, pp. 847-868. http://www.numdam.org/item/ASNSP_2003_5_2_4_847_0/
[1] Convex viscosity solutions and state constraints, J. Math. Pures Appl. (76) 9 (1997), 265-288. | MR 1441987 | Zbl 0890.49013
- - ,[2] “Functions of Bounded Variation and Free Discontinuity Problems”, Oxford Mathematical Monographs, Oxford Science Publications, Clarendon Press, Oxford, 2000. | MR 1857292 | Zbl 0957.49001
- - ,[3] Weak differentiability of BV functions on stratified groups, Math. Z. (1) 245 (2003), 123-153. | MR 2023957 | Zbl 1048.49030
- ,[4] Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric, Publ. Mat. 47 (2003), 237-259. | MR 1970902 | Zbl 1060.28002
- - ,[5] On -harmonic functions on the Heisenberg group, Comm. Partial Differential Equations 27 (2002), 727-762. | MR 1900561 | Zbl 1090.35063
,[6] Fully nonlinear elliptic equations, AMS colloquium publications 43, AMS, Providence, RI, 1995. | MR 1351007 | Zbl 0834.35002
- ,[7] Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. (2) 282 (1984), 487-502. | MR 732102 | Zbl 0543.35011
- - ,[8] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (1) 27 (1992), 1-67. | MR 1118699 | Zbl 0755.35015
- - ,[9] Subadditivity of homogeneous norms on certain nilpotent Lie groups, Proc. Amer. Math. Soc. 83 (1981), 69-70. | MR 619983 | Zbl 0475.43010
,[10] Notions of convexity in Carnot groups, Comm. Anal. Geom. (2) 11 (2003), 263-341. | MR 2014879 | Zbl 1077.22007
- - ,[11] The theorem of Busemann-Feller-Alexandrov in Carnot groups, preprint. | MR 2104079 | Zbl 1071.22004
- - - ,[12] “Measure Theory and Fine Properties of Functions”, Studies in Advanced Mathematics, CRC Press, 1992. | MR 1158660 | Zbl 0804.28001
- ,[13] “Fractal Geometry: Mathematical Foundations and Applications”, John Wiley & Sons, 1990. | MR 1102677 | Zbl 0689.28003
,[14] Maximum and comparison principles for convex functions on the Heisenberg group, preprint. | MR 2103838 | Zbl 1056.35033
- ,[15] On the second order derivatives of convex functions on the Heisenberg group, preprint. | Numdam | MR 2075987
- ,[16] Superharmonicity of nonlinear ground states, Rev. Math. Iberoam. 16 (2000), 17-27. | MR 1768532 | Zbl 0965.31002
- - ,[17] Convex functions on the Heisenberg group, to appear in Calc. Var. Partial Differential Equations. | MR 2027845 | Zbl 1072.49019
- - ,[18] Lipschitz continuity, Aleksandrov theorem and characterizations for H-convex functions, preprint. | MR 2208954 | Zbl 1115.49004
,[19] “Geometry of Sets and Measures in Euclidean Spaces. Fractals and Rectifiability”, Cambridge Studies in Advanced Mathematics, Cambridge University Press, 1995. | MR 1333890 | Zbl 0819.28004
,[20] A version of the Hopf-Lax formula in the Heisenberg group, Comm. Partial Differential Equations 27 (2002), 1139-1159. | MR 1916559 | Zbl 1080.49023
- ,[21] Métriques de Carnot-Carathéodory et quasiisométries des espaces symmétriques de rang un, Ann. Math. 129 (1989), 1-60. | MR 979599 | Zbl 0678.53042
,