Geodesic
Singular perturbations for a subelliptic operator
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1429-1451 Cet article a éte moissonné depuis la source Numdam

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We study some classes of singular perturbation problems where the dynamics of the fast variables evolve in the whole space obeying to an infinitesimal operator which is subelliptic and ergodic. We prove that the corresponding ergodic problem admits a solution which is globally Lipschitz continuous and it has at most a logarithmic growth at infinity. The main result of this paper establishes that, as ϵ → 0, the value functions of the singular perturbation problems converge locally uniformly to the solution of an effective problem whose operator and terminal data are explicitly given in terms of the invariant measure for the ergodic operator.

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DOI : 10.1051/cocv/2017063
Classification : 35B25, 49L25, 35J70, 35H20, 35R03, 35B37, 93E20
Keywords: Subelliptic equations, Heisenberg group, invariant measure, singular perturbations, viscosity solutions, degenerate elliptic equations

Mannucci, Paola 1 ; Marchi, Claudio 1 ; Tchou, Nicoletta 1

1 
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     title = {Singular perturbations for a subelliptic operator},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1429--1451},
     year = {2018},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {4},
     doi = {10.1051/cocv/2017063},
     zbl = {1414.35019},
     mrnumber = {3922437},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017063/}
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Mannucci, Paola; Marchi, Claudio; Tchou, Nicoletta. Singular perturbations for a subelliptic operator. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1429-1451. doi: 10.1051/cocv/2017063

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