Partial Differential Equations 2

Beschreibung

This encyclopedic work covers Partial Differential Equations of the elliptic, parabolic, and hyperbolic type in two and several variables. While partial differential equations are solved via integral representations in the preceding volume, this second volume uses functional analytic solution methods.

This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEs and complex variable methods.

In this second volume 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 with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, functional analytic methods are used in this volume.

This textbook can be chosen for a course over several semesters on a medium level. Advanced readers may study each chapter independently from the others.

Connects clearly PDEs and complex variable methods

The exposition is very careful and readable

Encyclopedia-like book on the subject

This comprehensive two-volume textbook covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses the following topics: 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, functional analytic solution methods are used in this volume.

Autor*in

Friedrich Sauvigny

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Banach Space Differential Geometry Hilbert space Nonlinear Elliptic Systems Partial Differential Equations partial differential equation

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