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Viscosity convex functions on Carnot groups


Author: Changyou Wang
Journal: Proc. Amer. Math. Soc. 133 (2005), 1247-1253
MSC (2000): Primary 58J05
DOI: https://doi.org/10.1090/S0002-9939-04-07836-0
Published electronically: November 19, 2004
MathSciNet review: 2117228
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Abstract: We prove that any upper semicontinuous v-convex function in any Carnot group is h-convex.


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  • [B] T. Bieske, On $\infty $-harmonic functions on the Heisenberg group. Comm. Partial Differential Equations 27 (2002), no. 3-4, 727-761. MR 1900561 (2003g:35033)
  • [BR] Z. Balogh, M. Rickly, Regularity of convex functions on Heisenberg groups. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 2 (2003), no. 4, 847-868. MR 2040646
  • [CC] X. Cabré, L. Caffarelli, Fully nonlinear elliptic equations. AMS Colloquium Publications 43, AMS, Providence, RI, 1995. MR 1351007 (96h:35046)
  • [CIL] M. Crandall, H. Ishii, P. L. 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 (92j:35050)
  • [DGN] D. Danielli, N. Garofalo, D. Nhieu, Notations of convexity in Carnot groups. Comm. Anal. Geom. 11 (2003), no. 2, 263-341. MR 2014879 (2004m:22014)
  • [EG] L. Evans, R. Gariepy, Measure theory and fine properties of functions. CRC Press, 1992. MR 1158660 (93f:28001)
  • [FS] G. Folland, E. Stein, Hardy spaces on homogeneous groups. Mathematical Notes, 28. Princeton University Press, Princeton, N.J., 1982. MR 0657581 (84h:43027)
  • [JLS] R. Jensen, P. L. Lions, P. 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 0934877 (89f:35027)
  • [JLMS] P. Juutinen, G. Lu, J. Manfredi, B. Stroffolini. In preparation.
  • [LMS] G. Lu, J. Manfredi, B. Stroffolini, Convex functions on the Heisenberg group. Calc. Var., 19 (2004), no. 1, 1-22. MR 2027845
  • [W] 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.

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Additional Information

Changyou Wang
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506

DOI: https://doi.org/10.1090/S0002-9939-04-07836-0
Received by editor(s): August 21, 2003
Published electronically: November 19, 2004
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2004 American Mathematical Society

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