## Md. Azizul Baten

# On the smoothness of solutions of
linear-quadratic regulator for degenerate diffusions

## (Lobachevskii Journal of Mathematics, Vol.17, pp.11 - 23)

The paper studies the smoothness of solutions of the
degenerate
Hamilton-Jacobi-Bellman (HJB) equation associated
with a linear-quadratic regulator control problem.
We establish the existence of a classical solution of the degenerate
HJB equation associated with this problem
by the technique of viscosity
solutions, and
hence derive an optimal control from the optimality conditions in the HJB equation.

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