Nonlinear Elliptic Equations of the Second OrderQing HanLabel: American Mathematical SocietyDescription: Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular much of the progress in the area in the twentieth century was driven by geometric applications from the Bernstein problem to the existence of Kahler-Einstein metrics. This book designed as a textbook provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampere equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality the book aims at providing self-contained clear and ``elementary'' proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.
