On the continuity of the solutions to the $L_p$ torsional Minkowski problem

In this paper, we derive the continuity of solutions to the $L_p$ torsional Minkowski problem for $p>1$. It is shown that the weak convergence of the $L_p$ torsional measure implies the convergence of the sequence of the corresponding convex bodies in the Hausdorff metric. Furthermore, continuity of the solution to the $L_p$ torsional Minkowski problem with regard to $p$ is also obtained.