On Some Fully Nonlinear Elliptic Equations

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

Proposal DMS-0401118 PI: Yanyan Li (Rutgers University) Title: On some fully nonlinear elliptic equations The PI proposes to work on some conformally invariant fully nonlinear equations which arise naturally from conformal geometry. In particular he proposes to prove a very general fully nonlinear version of the Yamabe conjecture. The corresponding Liouville type theorem has been established. The main task is to obtain apriori estimates for solutions. Partial differential equations arise naturally from physics, geometry, and many other fields and form a basis for mathematical modeling of the physical world. The proposed research should enhance the understanding of fully nonlinear elliptic equations, an important class of equations in modeling the physical world. The study of conformally invariant equations has found applications in geometry and topology. Part of the proposed work concerns important analytical issues for such equations. We expect that further applications to geometry and topology can be made with conformally invariant fully nonlinear equations and related ones, and the proposed work should provide analytical tools for such applications.