One of the central problems in mathematics and engineering is to study the behaviour of elastic structures. Of particular importance is to find an optimal way to distribute a given amount of elastic material whose resistance to the applied force is maximal. The mathematical description of (different types of) the above problem is what we refer to as a mass optimization problem (MOP). The study of MOP from the mathematical viewpoint will be the main topic of this project in pure mathematics. We aim to consider MOP within different ambient spaces: Euclidean, curved, and possibly non-smooth or infinite-dimensional - all belonging to the broad class of the so-called metric measure spaces. Towards this aim, we will use and develop further the theory of weakly differentiable functions. The project will take place at the University of Jyväskylä, at the Department of Mathematics and Statistics. Standard methods in mathematics will be used, relying on mathematical texts.

2024

2029