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Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 112-128 Cet article a éte moissonné depuis la source Numdam

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We study the partial differential equation         max{Lu - f, H(Du)} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.

DOI : 10.1051/cocv/2012001
Classification : 35J15, 49L25, 35R35, 49L20
Keywords: HJB equation, gradient constraint, free boundary problem, singular control, penalty method, viscosity solutions 
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     author = {Hynd, Ryan},
     title = {Analysis of {Hamilton-Jacobi-Bellman} equations arising in stochastic singular control},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {112--128},
     year = {2013},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     doi = {10.1051/cocv/2012001},
     mrnumber = {3023063},
     zbl = {1259.49043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012001/}
}
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Hynd, Ryan. Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 112-128. doi: 10.1051/cocv/2012001

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