Partial regularity of semiconvex viscosity supersolutions to fully nonlinear elliptic HJB equations and applications to stochastic control

In this note, we demonstrate that a locally semiconvex viscosity supersolution to a possibly degenerate fully nonlinear elliptic Hamilton-Jacobi-Bellman (HJB) equation is differentiable along the directions spanned by the range of the coefficient associated with the second-order term. The proof leve