This project is concerned with the regularity theory for a class of nonlinear elliptic equations and associated variational problems involving derivatives of the rearrangement of solutions, as well as related questions concerning convex symmetrization. The main emphasis is to be placed on variational problems which are approximable by sequences of multilayer free boundary problems. Regularity and structure of the level surfaces of solutions will be studied. This project has been motivated by a model of quasi static equilibrium of confined toroidal plasmas in thermonuclear fusion research, and the study of rotational fluid flow. The technical questions to be addressed have fundamental implications in areas such as fusion energy.
