For readers who have completed their study of linear elliptic differential equations and intend to explore nonlinear ones, Han discusses quasilinear and fully nonlinear equations, focusing on two important nonlinear elliptic differentials closely related to geometry, the mean curvature equation and the Monge-Ampére equation. He discusses in detail the Dirichlet problems for quasilinear and fully nonlinear elliptic equations of the second order: quasilinear uniformly elliptic equations in arbitrary domains, mean curvature equations in domains with non-negative boundary mean curvature, fully nonlinear uniformly elliptic equations in arbitrary domains, and Monge-Ampére equation in uniformly convex domains. Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)
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Qing Han, University of Notre Dame, IN, USA.
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Hardback. Zustand: New. 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. Bestandsnummer des Verkäufers LU-9781470426071
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