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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.
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.
From the reviews of the second edition:
"The second volume of the revised edition of this book presents functional analytic methods and applications to problems in differential geometry. ... The book will be a useful addition to the libraries of all those interested in the theory and applications of partial differential equations." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1246, 2012)
"The second volume of the revised edition of this book presents functional analytic methods and applications to problems in differential geometry. ... The book will be a useful addition to the libraries of all those interested in the theory and applications of partial differential equations." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1246, 2012)