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.
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From the reviews:
“The author’s aim is to present the entire domain Partial Differential Equations to students at an intermediate level. ... it is a carefully written treatise and with its quite non-standard choice of topics provides a welcome addition to the textbook literature on partial differential equations.” (M. Kunzinger, Monatshefte für Mathematik, Vol. 154 (1), May, 2008)Operators in Banach Spaces.- Linear Operators in Hilbert Spaces.- Linear Elliptic Differential Equations.- Weak Solutions of Elliptic Differential Equations.- Nonlinear Partial Differential Equations.- Nonlinear Elliptic Systems.
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