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KERNEL FUNCTIONS AND ELLIPTIC DIFFERENTIAL EQUATIONS IN MATHEMATICAL PHYSICSPDF|Epub|txt|kindle电子书版本网盘下载
- STEFAN BERGMAN AND M. SCHIFFER 著
- 出版社： ACADEMIC PRESS INC. PUBLISHERS
- ISBN：
- 出版时间：1953
- 标注页数：432页
- 文件大小：13MB
- 文件页数：437页
- 主题词：
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图书目录
Part A Boundary Value Problems for Partial Differential Equations of Elliptic Type1
CHAPTER Ⅰ：THEORY OF HEAT CONDUCTION1
1．The differential equation of heat transfer1
2．The special case of steady flow3
3．Point sources and fundamental singularities7
4．Fundamental solutions10
5．Discontinuities15
6．Dirichlet＇s principle17
7．A modified heat equation20
8．Formal considerations22
CHAPTER Ⅱ：FLUID DYNAMICS25
1．The fundamental equations25
2．Stationary irrotational flow28
3．Incompressible，irrotational，stationary fluid flow30
4．Sources and sinks32
5．Fundamental solutions and flow patterns35
6．Infinite domains38
7．Virtual mass43
8．Dirichlet identities46
9．Virtual mass as an extremum55
10．Variational formulas58
11．Free boundaries，discontinuity surfaces，and virtual mass64
12．Two-dimensional flows71
13．Boundary value problems and fundamental solutions in plane flows76
14．Obstacles in a plane flow82
15．The variation of the Green＇s function93
16．Lavrentieff＇s extremum problem for lift98
17．Free boundaries in plane flow101
18．The complex kernel function and its applications109
19．Axially symmetric motion of an incompressible fluid119
20．Associated partial differential equations124
21．Two-dimensional compressible fluid flow128
22．Construction of solutions of the differential equations in the hodograph plane133
23．The hodograph method and boundary value problems in the physical plane141
24．Singularities in the hodograph plane and their application147
CHAPTER Ⅲ．ELECTRO-AND MAGNETOSTATICS155
1．The general equations of the electrostatic field155
2．Conductor potentials and induction coefficients157
3．The energy of the electrostatic field160
4．The magnetostatic field165
5．The conductor potential；spherical harmonics178
6．Polarization of a conducting surface188
7．Forces and moments in a conductor surface193
8．Orthogonal harmonic functions198
CHAPTER Ⅳ：ELASTICITY206
1．Strain tensor fields206
2．Stress tensor fields209
3．Stress-strain relations211
4．The energy integral and boundary value problems215
5．Betti＇s formula and the fundamental singularity219
6．Fundamental solutions222
7．Construction of the fundamental solutions in terms of orthonormal solution fields226
8．Particular solutions229
9．The theory of thin plates232
10．Fundamental solutions of the biharmonic equation236
11．Plane strain246
Part B Kernel Function Methods in the Theory of Boundary Value Problems258
CHAPTER Ⅰ：PROPERTIES OF SOLUTIONS258
1．Introduction258
2．Notation and definitions259
3．Properties of the solutions of(1．1)261
4．Existence theorems for certain solutions262
5．Fundamental singularities and fundamental solutions268
6．Dirichlet integrals and fundamental functions273
CHAPTER Ⅱ：THE KERNEL FUNCTIONS AND THEIR PROPERTIES275
1．Kernel functions275
2．Orthonormal systems and construction of the kernel280
3．Integral operators and the construction of complete sets of solutions286
4．Dirichlet identities297
5．Choice of the fundamental singularity301
6．The regularity of l(P，Q)303
7．An integral equation for the kernel309
8．The eigenvalues of the kernel l(P，Q)315
9．Series developments and integral equations326
CHAPTER Ⅲ：VARIATIONAL AND COMPARISON THEORY335
1．Relations between kernels of different domains335
2．Eigenfunctions of the γ-transformation346
3．Doubly orthogonal systems351
4．An application of the operators to the theory of orthogonal functions355
5．Comparison formulas for Green＇s and Neumann＇s functions357
6．Variational theory360
CHAPTER Ⅳ：EXISTENCE THEORY371
1．Boundary value problem and orthogonal projection371
CHAPTER Ⅴ：DEPENDENCE OF KERNELS ON BOUNDARY CONDITIONS AND THE DIFFERENTIAL EQUATION381
1．The positiveness of the fundamental functions381
2．Stability of fundamental functions384
3．Stability of eigenvalues388
4．Construction of a fundamental singularity392
CHAPTER Ⅵ：GENERALIZATIONS395
1．Different types of metrics395
2．Further generalizations402
List of Symbols Used in Part B404
Bibliography Books408
Articles412
Author Index421
Subject Index425