This project will study solutions to elliptic equations derived from multiple integrals with symmetries. The topics to be emphasized are estimates up to the boundary, global regularity, isolated and removable singularities, apriori gradient estimates, and the relation between quasiconvexity and rank one convexity. The equations to be studied model phenomena in geometry, optimal design and nonlinear elasticity. Thus this project has applications in various branches of mathematics and engineering.
