Partial Differential Equations: An Introduction

Front Matter....Pages N2-xi
Front Matter....Pages 1-1
Introduction....Pages 3-10
The Wave Equation....Pages 11-27
The Potential Equation....Pages 28-42
The Heat Equation....Pages 43-56
Front Matter....Pages 57-57
Differential Equations of the Second Order....Pages 59-68
Systems of Differential Equations of the First Order....Pages 69-80
On the Necessity of Classification Into Types....Pages 81-86
Front Matter....Pages 87-87
Elliptic and Elliptic-Parabolic Type....Pages 89-98
Parabolic Type....Pages 99-101
Hyperbolic Type....Pages 102-114
Mixed Type....Pages 115-121
Front Matter....Pages 123-123
Equations of Hyperbolic Type in Two Independent Variables....Pages 125-150
Boundary and Initial-Value Problems for Equations of Hyperbolic and Parabolic Type in Two Independent Variables....Pages 151-171
Equations of Elliptic Type....Pages 172-194
Weyl’s Lemma for Equations of Elliptic Type....Pages 195-205
Front Matter....Pages 207-207
Auxiliary Tools....Pages 209-217
Schauder’s Technique of Proof for Existence Problems in Elliptic Differential Equations....Pages 218-221
The Regular Eigenvalue Problem....Pages 222-231
Elliptic Systems of Differential Equations....Pages 232-250
Back Matter....Pages 251-261