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Other titles in the Dover Books on Mathematics series:
Abstract Methods in Partial Differential Equations (Dover Books on Mathematics)by Robert W Carroll
Synopses & Reviews
This self-contained text is directed to graduate students with some previous exposure to classical partial differential equations. Readers can attain a quick familiarity with various abstract points of view in partial differential equations, allowing them to read the literature and begin thesis work. The author's detailed presentation requires no prior knowledge of many mathematical subjects and illustrates the methods' applicability to the solution of interesting differential problems.
The treatment emphasizes existence-uniqueness theory as a topic in functional analysis and examines abstract evolution equations and ordinary differential equations with operator coefficients. A concluding chapter on global analysis develops some basic geometrical ideas essential to index theory, overdetermined systems, and related areas. In addition to exercises for self-study, the text features a thorough bibliography. Appendixes cover topology and fixed-point theory in addition to Banach algebras, analytic functional calculus, fractional powers of operators, and interpolation theory.
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Detailed and self-contained, this treatment is directed to graduate students with some previous exposure to classical partial differential equations. The author examines a variety of modern abstract methods in partial differential equations, especially in the area of abstract evolution equations. Additional topics include the theory of nonlinear monotone operators applied to elliptic and variational problems. 1969 edition.
Table of Contents
1. Functional Analysis and Distributions
2. Elliptic Theory
3. Evolution Equations I
4. Evolution Equations II
5. Evolution Equations III
6. Global Analysis
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