Remarks on convexity estimates for solutions of the torsion problem

In this paper,for the solution of the torsion problem about the equation Δu=-2 with homogeneous Dirichlet boundary conditions in a bounded convex domain in Rn,we find a superharmonic function which implies the strict concavity of u ^(1/2) and give some convexity estimates.It is a generalization of Makar-Limanov’s result(Makar-Limanov(1971))and Ma-Shi-Ye’s result(Ma et al.(2012)).