Abstract.
Convex functions in Euclidean space can be characterized as universal viscosity subsolutions of all homogeneous fully nonlinear second order elliptic partial differential equations. This is the starting point we have chosen for a theory of convex functions on the Heisenberg group.
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Received: 5 July 2002, Accepted: 24 October 2002, Published online: 6 June 2003
Mathematics Subject Classification (1991):
49L25, 35J70, 35J67, 22E30
Guozhen Lu: First author supported by US NSF grant DMS-9970352
Juan J. Manfredi: Second author supported by US NSF grant DMS-0100107
Bianca Stroffolini: Third author was supported by G.N.A.M.P.A. and by the 2002 project”Partial Differential Equations and Control Theory”
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Lu, G., Manfredi, J.J. & Stroffolini, B. Convex functions on the Heisenberg group. Cal Var 19, 1–22 (2003). https://doi.org/10.1007/s00526-003-0190-4
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DOI: https://doi.org/10.1007/s00526-003-0190-4