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.

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 : https://doi.org/10.1051/cocv/2012001
Classification : 35J15,  49L25,  35R35,  49L20
Mots clés : 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},
     publisher = {EDP-Sciences},
     volume = {19},
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     year = {2013},
     doi = {10.1051/cocv/2012001},
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     language = {en},
     url = {http://www.numdam.org/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. http://www.numdam.org/articles/10.1051/cocv/2012001/

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