Optimization Problem Over the Space of Functions with Second Order Bounded Variation

This talk is a discussion about the extremal points of the unit ball with respect to the Hessian-Schatten variation seminorm, i.e. the total variation of the second distributional differential with respect to the Schatten matrix norm. The main result is an approximation result of these extremal points with continous and piecewise affine extremal points. Based on a work with L. Ambrosio, S. Aziznejad and M. Unser and on a work with L. Ambrosio and S. Conti.