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Provides a complete and thorough introduction into the theory of linear and nonlinear partial differential equations
Presents interesting applications to physics and differential geometry
Includes the basic methods from linear and nonlinear functional analysis
This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.
In this second volume, special emphasis is placed on functional analytic methods and applications to differential geometry. The following topics are treated:
solvability of operator equations in Banach spaces
linear operators in Hilbert spaces and spectral theory
Schauder's theory of linear elliptic differential equations
weak solutions of differential equations
nonlinear partial differential equations and characteristics
nonlinear elliptic systems
boundary value problems from differential geometry
This new second edition of this volume has been thoroughly revised and a new chapter on boundary value problems from differential geometry has been added.
In the first volume, partial differential equations by integral representations are treated in a classical way.
This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.
Content Level »Research
Keywords »Monge-Ampère equations - Schauder's continuity method - degree of mapping in Banach spaces - nonlinear elliptic systems and H-surfaces - spectral theory - weak solutions and regularity