There are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. 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.
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.
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana.
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.