This project involves research on nonconvex variational problems, singular perturbation, and nonlinear partial differential equations. The connections between nonconvex problems and the "relaxed problems" obtained by introducing a convex perturbation will be analyzed, as well as the connections between variational problems and the gradient flows they generate. Particular cases to be emphasized are variational problems depending on a gradient, locally area-minimizing partitions, flows driven by mean curvature, and optimal design via least gradient. The results of this project will lead to better understanding of physical problems related to material instabilities, which in turn will help in the development of new materials. ***
