Free access
Issue
ESAIM: COCV
Volume 13, Number 1, January-March 2007
Page(s) 107 - 119
DOI http://dx.doi.org/10.1051/cocv:2007005
Published online 14 February 2007
  1. O. Alvarez, and M. Bardi, Viscosity solutions methods for singular perturbations in deterministic and stochastic control. SIAM J. Control Optim. 40 (2001) 1159–1188. [CrossRef] [MathSciNet]
  2. M. Arisawa, Quasi-periodic homogenizations for second-order Hamilton-Jacobi-Bellmann equations. Adv. Sci. Appl. 11 (2001) 465–480.
  3. M. Bardi and I. Capuzzo Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser Boston, Boston, MA (1997).
  4. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Math. Appl. 17 (1994).
  5. A. Bellaïche and J.-J. Risler, ed., Sub-Riemannian Geometry. Birkhäuser, Progress. Math. 144 (1996).
  6. I. Birindelli and J. Wigniolle, Homogenization of Hamilton-Jacobi equations in the Heisenberg Group. Commun. Pure Appl. Anal. 2 (2003) 461–479. [CrossRef] [MathSciNet]
  7. I. Capuzzo Dolcetta and H. Ishii, On the rate of convergence in homogenization of Hamilton-Jacobi equations. Indiana University Math. J. 50 (2001) 1113–1129. [CrossRef]
  8. L.C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinburgh 11A (1989) 359–375.
  9. L.C. Evans, Periodic homogenization of certain fully nonlinear PDE. Proc. Roy. Soc. Edinburgh 120 (1992) 245–265.
  10. G.B. Folland and E.M. Stein, Hardy spaces on homogeneous groups. Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo. Math. Notes 28 (1982)
  11. H. Ishii, Perron's method for Hamilton-Jacobi equations. Duke Math. J. 55 (1987) 369–384. [CrossRef] [MathSciNet]
  12. P. Juutinen, G. Lu, J. Manfredi and B. Stroffolini, Convex functions on Carnot Groups, to appear in Revista Mathematica Iberoamericana.
  13. G. Lu, J. Manfredi and B. Stroffolini, Convex functions on the Heisenberg Group. Calc. Var. Partial Differential Equations 19 (2004) 1–22. [CrossRef] [MathSciNet]
  14. P.L. Lions, G. Papanicolau and R.S. Varadhan, Homogenization of Hamilton-Jacobi equations, preprint (1986).
  15. J. Manfredi, Nonlinear subelliptic equations on Carnot Groups. Notes of a course at the School on Analysis and Geometry, Trento (2003).
  16. J. Manfredi and B. Stroffolini A Version of the Hopf-Lax Formula in the Heisenberg Group. Comm. in Partial Differential Equations 27 (2002) 1139–1159.
  17. R. Montgomery, A Tour of Subriemannian Geometries, their geodesics and applications. American Mathematical Society, Providence, RI. Math. Surveys Monographs 91(2002).
  18. R. Monti and F. Serra Cassano, Surface measures in Carnot-Carathéodory spaces. Calc. Var. 13 (2001) 339-376. [CrossRef]
  19. D. Morbidelli, Fractional Sobolev norms and structure of Carnot-Caratheodory balls for Hörmander vector fields. Studia Math. 139 (2000) 213–244. [MathSciNet]
  20. A. Nagel, E.M. Stein and S. Wainger, Balls and metrics defined by vector fields I: basic properties. Acta Math. 137 (1976) 247–320. [CrossRef] [MathSciNet]