Nonlinear Elliptic Equations and Applications

Nonlinear models dominate the frontline of modern theoretical and applied mathematics. During the last decade there has been an explosion in the prominence of models based on nonlinear elliptic partial differential equations in conjunction with applications to optimal transportation and geometric analysis. This proposal is multistranded and will consider applications to optimal transportation, second order variational problem, conformal geometry, potential theory and curvature problems, building upon major breakthroughs by the proposers in previous grant research.