Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things about it--it is a wonderful book. --Tobias Colding This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. 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. This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations.
First Order Elliptic Systems: A Function Theoretic Approach
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations.
The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.
This is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations.
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations.
Recent results for asymmetric nonlinear boundary value problems / D. Arcoya -- Connecting orbits of Hamiltonian systems / S.V. Bolotin -- Morse theory in nonlinear analysis / K.-C. Chang -- Critical point theory and applications to elliptic ...
Second Order Elliptic Equations and Elliptic Systems
... Conformally invariant powers of the Laplacian. I. Existence. J. London Math. Soc. 46, (1992), 557-565. [16] Graham, C.R; Zworski, M. Scattering matrix in conformal geometry. Invent. Math. 152, (2003), no. 1, 89-118. [17] Hamilton, R.S. ...
This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations.
Intended mainly for use as a reference manual, this edition encompasses all the improvements of the newest version of the PLTMG software package. This updated version introduces several significant changes.