Viscosity convex functions on Carnot groups
HTML articles powered by AMS MathViewer
- by Changyou Wang PDF
- Proc. Amer. Math. Soc. 133 (2005), 1247-1253 Request permission
Abstract:
We prove that any upper semicontinuous v-convex function in any Carnot group is h-convex.References
- Thomas Bieske, On $\infty$-harmonic functions on the Heisenberg group, Comm. Partial Differential Equations 27 (2002), no. 3-4, 727–761. MR 1900561, DOI 10.1081/PDE-120002872
- Zoltán M. Balogh and Matthieu Rickly, Regularity of convex functions on Heisenberg groups, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 4, 847–868. MR 2040646
- Luis A. Caffarelli and Xavier Cabré, Fully nonlinear elliptic equations, American Mathematical Society Colloquium Publications, vol. 43, American Mathematical Society, Providence, RI, 1995. MR 1351007, DOI 10.1090/coll/043
- Michael G. Crandall, Hitoshi Ishii, and Pierre-Louis Lions, User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 1, 1–67. MR 1118699, DOI 10.1090/S0273-0979-1992-00266-5
- Donatella Danielli, Nicola Garofalo, and Duy-Minh Nhieu, Notions of convexity in Carnot groups, Comm. Anal. Geom. 11 (2003), no. 2, 263–341. MR 2014879, DOI 10.4310/CAG.2003.v11.n2.a5
- Lawrence C. Evans and Ronald F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1158660
- G. B. Folland and Elias M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, vol. 28, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1982. MR 657581
- R. Jensen, P.-L. Lions, and P. E. Souganidis, A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations, Proc. Amer. Math. Soc. 102 (1988), no. 4, 975–978. MR 934877, DOI 10.1090/S0002-9939-1988-0934877-2
- P. Juutinen, G. Lu, J. Manfredi, B. Stroffolini. In preparation.
- Guozhen Lu, Juan J. Manfredi, and Bianca Stroffolini, Convex functions on the Heisenberg group, Calc. Var. Partial Differential Equations 19 (2004), no. 1, 1–22. MR 2027845, DOI 10.1007/s00526-003-0190-4
- C. Y. Wang, The Aronsson equation for absolute minimizers of $L^{\infty }$-functionals associated with vector fields satisfying Hörmander’s condition. To appear in Trans. Amer. Math. Soc.
Additional Information
- Changyou Wang
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
- Received by editor(s): August 21, 2003
- Published electronically: November 19, 2004
- Communicated by: David S. Tartakoff
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1247-1253
- MSC (2000): Primary 58J05
- DOI: https://doi.org/10.1090/S0002-9939-04-07836-0
- MathSciNet review: 2117228