Complex Analytic Methods for Partial Differential Equations: An Introductory Text

Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Dedication......Page 6
Preface......Page 8
Table of Contents......Page 0
1.1. CAUCHY integral......Page 12
1.2. GREEN functions and SCHWARZ operators......Page 29
1.3. RIEM A N N boundary value problem......Page 49
1.4. RIEMANN-HILBERT boundary value problem......Page 56
2.1. Integral representations......Page 80
2.2. Properties of integral operators......Page 85
3.1. Generalized BELTRAMI equation......Page 110
3.2. RIEMA N N boundary value problem......Page 125
3.3. RIEMANN-HILBERT boundary value problem......Page 129
3.4. POINCARE boundary value problem......Page 155
3.5. Discontinuous boundary value problems......Page 160
4.1. Initial boundary value problem for pseudoparabolic equations......Page 186
4.2. Initial boundary value problem for a composite type system......Page 195
4.3. Entire solution to nonlinear generalized BELTRAMI equations......Page 205
5.1. Elliptic second order equations......Page 214
5.2. Higher order equations......Page 244
5.3. First order systems in two complex variables with analytic coefficients......Page 250
5.4. The SCHWARZ-POISSON formula for polydiscs......Page 263
References......Page 268
Index of Names......Page 278
Index of Subjects......Page 280
Index of Corollaries, Definitions, Lemmas, Theorems......Page 284
Back Cover......Page 285