On some properties of convex functions (Q5905616)

Summary: We summarize recent results of a research concerning the singularities (non-differentiability points) of convex functions. This research covers various aspects, from the estimate of the Hausdorff dimension of some kinds of singularities to the study of their propagation. We study also semicontinuity and relaxation problems related to the area of the graph of the gradient of a convex function and the existence of weak determinants of the minors of the Hessian matrix.