Partial Differential Equations 2: Functional Analytic Methods (Universitext)

Sauvigny, Friedrich

ISBN 10: 3540344616 / ISBN 13: 9783540344612

Published by Springer, 2006

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Bibliographic Details

• Title: Partial Differential Equations 2: Functional Analytic Methods (Universitext)
• Publisher: Springer
• Publication Date: 2006
• Language: English
• ISBN 10: 3540344616
• ISBN 13: 9783540344612
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses 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 with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.

From the Back Cover

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.