Overview

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.

Full Product Details

9781470426071

Table of Contents

Reviews

“[T]he book of Han will serve as a valuable resource for graduate students and for anyone interested in the subject of nonlinear second order elliptic PDEs.” - Dian K. Palagachev, Zentralblatt MATH

[T]he book of Han will serve as a valuable resource for graduate students and for anyone interested in the subject of nonlinear second order elliptic PDEs. - Dian K. Palagachev, Zentralblatt MATH

Author Information

Qing Han, University of Notre Dame, IN, USA.

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