  We investigate the convexity problem for the Parisi functional defined on the
space of the so-called functional ordered parameters in the
Sherrington-Kirkpatrick model. In the recent work of Panchenko [3], he proved
that this functional is convex along one-sided directions with a probabilistic
method. In this paper, we will study this problem with a PDE approach that
simplifies his original proof and presents more general results.
