Foundations of the Classical Theory of Partial Differential Equations

• 1. Basic Concepts.- 1. Basic Definitions and Examples.- 2. The Cauchy-Kovalevskaya Theorem and Its Generalizations.- 3. Classification of Linear Differential Equations. Reduction to Canonical Form and Characteristics.- 2. The Classical Theory.- 1. Distributions and Equations with Constant Coefficients.- 2. Elliptic Equations and Boundary-Value Problems.- 3. Sobolev Spaces and Generalized Solutions of Boundary-Value Problems.- 4. Hyperbolic Equations.- 5. Parabolic Equations.- 6. General Evolution Equations.- 7. Exterior Boundary-Value Problems and Scattering Theory.- 8. Spectral Theory of One-Dimensional Differential Operators.- 9. Special Functions.- References.- Author Index.

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