This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame (IN). Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear, however, the presented methods also apply to nonlinear problems. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Elliptic Partial Differential Equations (Courant Lecture Notes)

Science & Math

Lin, Fanghua

Han, Qing

Mathematics

New York Univ Courant Inst

Since the publication of the seminal work of H. Federer which gives a rather complete and comprehensive discussion on the subject, the geometric measure theory has developed in the last three decades into an even more cohesive body of basic knowledge with an ample structure of its own, establishing strong ties with many other areas of mathematics and made numerous new striking applications. The present book is intended for the researchers in other fields of mathematics as well as graduate students for a quick overview on the subject of the geometric measure theory emphasizing on various basic ideas, techniques and their applications in problems arising in the calculus of variations, geometrical analysis and nonlinear partial differential equations. This graduate-level treatment of Geometric Measure Theory illustrates with concrete examples and emphasizes basic ideas and techniques with their applications to the calculus of variations, geometrical analysis, and nonlinear PDEs. The book, in addition to a full index and bibliography, include eight main chapters. New paperback re-issue.

Geometric Measure Theory: An Introduction (2010 re-issue)

Yang, Xiaoping

International Press of Boston, Incorporated

This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and Bethuel, and weakly harmonic maps from Riemannian surfaces by Helein, as well as on the structure of a singular set of minimizing harmonic maps and stationary harmonic maps by Simon and Lin. The second part of the book contains a systematic coverage of heat flow of harmonic maps that includes Eells-Sampson's theorem on global smooth solutions, Struwe's almost regular solutions in dimension two, Sacks-Uhlenbeck's blow-up analysis in dimension two, Chen-Struwe's existence theorem on partially smooth solutions, and blow-up analysis in higher dimensions by Lin and Wang.The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis.

The Analysis of Harmonic Maps and Their Heat Flows

Wang, Changyou

World Scientific Publishing Company

See the best price to sell, buy, or rent books by Lin, Fanghua. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Lin, Fanghua