Partial differential equations

Inhaltsverzeichnis1. Examples.1. Introduction.2. The Wave Equation.3. The Potential Equation.4. The Heat Equation.2. Classification into Types, Theory of Characteristics, and Normal Form.1. Differential Equations of the First Order.2. Systems of Differential Equations of the First Order.3. On the Necessity of Classification Into Types.3. Questions of Uniqueness.1. Elliptic and Elliptic-Parabolic Type.2. Parabolic Type.3. Hyperbolic Type.4. Mixed Type.4. Questions of Existence.1. Equations of Hyperbolic Type in Two Independent Variables.2. Boundary and Initial-Value Problems for Equations of Hyperbolic and Parabolic Type in Two Independent Variables.3. Equations of Elliptic Type.4. Weyl’s Lemma for Equations of Elliptic Type.5. Simple Tools from Functional Analysis Applied to Questions of Existence.1. Auxiliary Tools.2. Schauder’s Technique of Proof for Existence Problems in Elliptic Differential Equations.3. The Regular Eigenvalue Problem.4. Elliptic Systems of Differential Equations.Solutions.