We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups. The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property.
Keywords: homogenization, Carnot groups, Hamilton-Jacobi
@article{COCV_2007__13_1_107_0, author = {Stroffolini, Bianca}, title = {Homogenization of {Hamilton-Jacobi} equations in {Carnot} groups}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {107--119}, publisher = {EDP-Sciences}, volume = {13}, number = {1}, year = {2007}, doi = {10.1051/cocv:2007005}, mrnumber = {2282104}, zbl = {1113.35020}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007005/} }
TY - JOUR AU - Stroffolini, Bianca TI - Homogenization of Hamilton-Jacobi equations in Carnot groups JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 107 EP - 119 VL - 13 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007005/ DO - 10.1051/cocv:2007005 LA - en ID - COCV_2007__13_1_107_0 ER -
%0 Journal Article %A Stroffolini, Bianca %T Homogenization of Hamilton-Jacobi equations in Carnot groups %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 107-119 %V 13 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007005/ %R 10.1051/cocv:2007005 %G en %F COCV_2007__13_1_107_0
Stroffolini, Bianca. Homogenization of Hamilton-Jacobi equations in Carnot groups. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 1, pp. 107-119. doi : 10.1051/cocv:2007005. http://www.numdam.org/articles/10.1051/cocv:2007005/
[1] Viscosity solutions methods for singular perturbations in deterministic and stochastic control. SIAM J. Control Optim. 40 (2001) 1159-1188. | Zbl
, and ,[2] Quasi-periodic homogenizations for second-order Hamilton-Jacobi-Bellmann equations. Adv. Sci. Appl. 11 (2001) 465-480. | Zbl
,[3] Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser Boston, Boston, MA (1997). | MR | Zbl
and ,[4] Solutions de viscosité des équations de Hamilton-Jacobi. Springer-Verlag, Math. Appl. 17 (1994). | MR | Zbl
,[5] MR
and , ed., Sub-Riemannian Geometry. Birkhäuser, Progress. Math. 144 (1996). |[6] Homogenization of Hamilton-Jacobi equations in the Heisenberg Group. Commun. Pure Appl. Anal. 2 (2003) 461-479. | Zbl
and ,[7] On the rate of convergence in homogenization of Hamilton-Jacobi equations. Indiana University Math. J. 50 (2001) 1113-1129.
and ,[8] The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinburgh 11A (1989) 359-375. | Zbl
,[9] Periodic homogenization of certain fully nonlinear PDE. Proc. Roy. Soc. Edinburgh 120 (1992) 245-265. | Zbl
,[10] Hardy spaces on homogeneous groups. Princeton University Press, Princeton, N.J., University of Tokyo Press, Tokyo. Math. Notes 28 (1982) | MR | Zbl
and ,[11] Perron's method for Hamilton-Jacobi equations. Duke Math. J. 55 (1987) 369-384. | Zbl
,[12] Convex functions on Carnot Groups, to appear in Revista Mathematica Iberoamericana. | MR | Zbl
, , and ,[13] Convex functions on the Heisenberg Group. Calc. Var. Partial Differential Equations 19 (2004) 1-22. | Zbl
, and ,[14] Homogenization of Hamilton-Jacobi equations, preprint (1986).
, and ,[15] Nonlinear subelliptic equations on Carnot Groups. Notes of a course at the School on Analysis and Geometry, Trento (2003).
,[16] A Version of the Hopf-Lax Formula in the Heisenberg Group. Comm. in Partial Differential Equations 27 (2002) 1139-1159. | Zbl
and[17] A Tour of Subriemannian Geometries, their geodesics and applications. American Mathematical Society, Providence, RI. Math. Surveys Monographs 91(2002). | MR | Zbl
,[18] Surface measures in Carnot-Carathéodory spaces. Calc. Var. 13 (2001) 339-376. | MR | Zbl
and ,[19] Fractional Sobolev norms and structure of Carnot-Caratheodory balls for Hörmander vector fields. Studia Math. 139 (2000) 213-244. | Zbl
,[20] Balls and metrics defined by vector fields I: basic properties. Acta Math. 137 (1976) 247-320. | Zbl
, and ,Cited by Sources: