Boundary value problems for elliptic equations and systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Longman Scientific
1990
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Pitman monographs and surveys in pure and applied mathematics
46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 411 S. |
| ISBN: | 0470213043 |
Internformat
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| 100 | 1 | |a Wen, Guo-Chun |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boundary value problems for elliptic equations and systems |c Guo Chun Wen ; Heinrich G. W. Begehr |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York u.a. |b Longman Scientific |c 1990 | |
| 300 | |a XII, 411 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 700 | 1 | |a Begehr, Heinrich G. W. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804118271728812032 |
|---|---|
| adam_text | Contents
Preface xi
CHAPTER I. BOUNDARY VALUE PROBLEMS FOR SIMPLE COMPLEX EQUATIONS 1
§ 1. Some boundary value problems for analytic functions 1
1. Formulation of the Riemann Hilbert boundary value
problem 2
2. Uniqueness of the solution W Problem B 4
3. A priori estimates of solutions for Problem B 6
4. Solvability of Problem B for analytic functions 11
5. The compound boundary valu e problem for analytic
functions 19
§ 2. Some boudary value problems for harmonic functions 22
1. Formulation and uniqueness of the regular oblique
derivative problem 22
2. A priori estimates of solutions for the regular oblique
derivative problem 26
3. Solvability of the regular oblique derivative problem 28
4. The irregular oblique derivative problem for harmonic
functions 34
§ 3. Some boundary value problems for simple first order
complex equations 37
1. Some proper modified propositions of the Riemann
Hilbert problem for (3.1) 37
2. Properties of solutions to Problem B* for analytic
functions 41
3. The homogeneous problem C? for simple complex
equations 46
4. Properties of boundary value problems for first order
complex equations 52
§ 4. Some boundary value problems for simple second order
equations 54
1. Some proper propositions of the oblique derivative
problem for (4.1) 54
2. Properties of solutions to Problem Q* and Problem Q**
for (4.1) 56
3. Properties of solutions to Problem P** and
Problem P*** for (4.1) 57
v
CHAPTER II. BOUNDARY VALUE PROBLEMS FOR ELLIPTIC COMPLEX
EQUATIONS OF FIRST ORDER 66
§ 1. Reductions of elliptic systems of two first order
equations 66
1. Reduction of linear elliptic systems of two first
order equations 66
2. Reduction of the quasilinear elliptic system of two
first order equations 73
3. Reduction of the nonlinear elliptic system of two
first order equations 74
4. Conditions for uniformly elliptic complex equations
of first order 78
§ 2. Properties of solutions to the elliptic complex equation
of first order 80
1. A representation theorem for solutions to complex
equations of first order 80
2. Another representation for solutions to the complex
equation of first order 86
3. The compactness principle for sequences of solutions
to complex equations 87
§ 3. The Haseman boundary value problem for elliptic complex
equations of first order 91
1. An existence theorem for solutions to the nonlinear
complex equation 91
2. Formulation and reduction of the Haseman boundary
value problem 98
3. Solvability of the Haseman boundary value problem 100
§ 4. The Riemann Hilbert problem for the elliptic complex
equation of first order 103
1. Formulation and uniqueness of the solution of the
Riemann Hilbert problem 103
2. A priori estimates of solutions for the Riemann
Hilbert problem 108
3. Solvability of the Riemann Hilbert problem for
nonlinear complex equations 114
4. The Riemann Hilbert problem for linear equations 118
§ 5. Applications of boundary value problems to nonlinear
quasiconformal mappings 121
1. Existence theorems for nonlinear quasiconformal
mappings 122
2. Uniqueness theorems for nonlinear quasiconformal
mappings for (5.3) 127
§ 6. The compound boundary value problem for the elliptic
complex equation 132
1. Formulation of the compound boundary value problem 132
2. The modified compound problem and a priori estimates
of its solutions 137
vi
3. Solvability of the compound boundary value problem 141
CHAPTER III. BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATIONS OF
SECOND ORDER 144
§ 1. Reduction of elliptic equations of second order 144
1. Complex form of linear and quasilinear elliptic
equations of second order 144
2. Complex form of nonlinear elliptic equations of
second order 147
3. Conditions for uniformly elliptic equations of
second order 149
§ 2. Extremum principles for elliptic equations of second
order 150
1. Extremum principles for equation (2.1) with
continuous coefficients 151
2. Extremum principles for equation (2.1) with
measurable coefficients 155
§ 3. The representation theorem and compactness principle
of solutions for equations of second order 159
1. Representation theorem of solutions for elliptic
equations of second order 159
2. The compectness principle of sequences of solutions
to second order equations 165
3. The Harnack inequality for positive solutions to
(2.20) 168
§ 4. The regular oblique derivative problem for elliptic
equations of second order 172
1. The Dirichlet problem for second order equations 172
2. Formualtion and uniqueness of the regular oblique
derivative problem for (1.24) 179
3. A priori estimates and existence of solutions to
Problem III for (1.24) 181
4. A priori estimates and existence of solutions to
Problem IV for (1.24) 188
§ 5. The irregular oblique derivative problem for elliptic
equations of second order 191
1. Formulation and uniqueness for the irregular oblique
derivative problem 191
2. A priori estimate of solutions for the irregular
oblique derivative problem 195
3. Solvability of the irregular oblique derivative
problem 198
§ 6. The Poincare boundary value problem for elliptic
equations of second order 206
1. The Poincare problem for nonlinear equations of
second order 206
vii
2. The Poincare problem for linear equations of second
order 212
CHAPTER IV. BOUNDARY VALUE PROBLEMS WITH PIECEWISE CONTINUOUS
COEFFICIENTS FOR ELLIPTIC EQUATIONS AND SYSTEMS 217
§ 1. Boundary value problems with piecewise continuous
coefficients for analytic functions 217
1. The Riemann Hilbert problem with piecewise
continuous coefficients in a simply connected domain 217
2. The Riemann Hilbert problem with piecewise
continuous coefficients in a multiply connected
domain 225
3. Integral representation and estimates of solutions
of Problem B* in a multiply connected domain 232
§ 2. The Riemann Hilbert problem with piecewise continuous
coefficients for complex equations of first order 236
1. Existence theorem for solutions to the nonlinear
elliptic complex equation of first order 236
2. The Riemann Hilbert problem with piecewise continuous
coefficients for complex equations of first order 241
3. Some existence theorems for nonlinear quasiconformal
mappings 24 7
§ 3. The Riemann boundary value problem with piecewise
continuous coefficients for complex equations of first
order 249
1. The Riemann boundary value problem with piecewise
continuous coefficients on closed curves 249
2. The Riemann boundary value problem for complex
equations of first order on open arcs 254
§ 4. The Poincare problem with piecewise continuous
coefficients for elliptic equations of second order 257
1. A priori estimates of solutions to the modified
Poincare problem with piecewise continuous
coefficients for (4.2) 258
2. Solvability of Problem Q* and the Problem P* for (4.1) 262
3. The mixed boundary value problem of elliptic equations
of second order 265
CHAPTER V. BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS OF TWO
SECOND ORDER EQUATIONS 273
§ 1. Reduction and conditions for elliptic systems of two
second order equations 273
1. Complex form of elliptic systems of two linear
equations of second order 273
2. Complex form of elliptic systems of two nonlinear
equations of second order 275
3. Conditions for uniformly elliptic complex equations
of second order 279
viii
§ 2. The Dirichlet problem and the Neumann problem for
elliptic complex equations of second order 281
1. Formulations of the Dirichlet problem and the Neumann
problem 281
2. Solvability of Problem 0 for the linear elliptic
complex equation 283
3. Solvability of Problem 0 for the nonlinear elliptic
complex equation 285
4. Solvability of Problem 0 of the nonlinear complex
system of second order 288
§ 3. The oblique derivative problem for elliptic complex
equations of second order 296
1. The oblique derivative problem for complex equations
of second order in the unit disc 297
2. The oblique derivative problem for nonlinear complex
equations of second order in a multiply connected
domain 302
3. The oblique derivative problem for linear complex
equations of second order in a multiply connected domain 309
4. The oblique derivative problem for nonlinear complex
equations of first order in a multiply connected
doma in 314
§ 4. The Riemann Hilbert problem of complex equations of
second order 319
1. Representation and estimation of solutions for the
Riemann Hilbert problem for second order complex
equations 319
2. Solvability of the Riemann Hilbert problem for second
order complex equations 326
§ 5. Boundary value problems for another class of second order
complex equations 329
CHAPTER VI. BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS OF
SEVERAL EQUATIONS 336
§ 1. Reductions of elliptic systems of several equations of
first and second order 336
1. Reduction of elliptic systems of several first order
equations 336
2. Reduction of elliptic systems of several second order
equations 341
3. Conditions for elliptic systems of complex equations
of first and second order 343
§ 2. Boundary value problems for nonlinear complex systems
of first order 348
1. Formulation of the Riemann Hilbert problem for
nonlinear complex systems of first order 348
2. A priori estimates of solutions for the Riemann Hilbert
problem 350
ix
3. Solvability of the Riemann Hilbert problem for
nonlinear complex systems of first order 354
§ 3. Boundary value problems for complex systems of several
linear equations of first and second order 359
1. The Riemann Hilbert problem for complex systems of
linear first order equations 359
2. The oblique derivative problem for complex systems
of linear second order equations 366
§ 4. The oblique derivative problem for complex systems of
nonlinear second order equations 373
1. Formulation of the oblique derivative problem and the
corresponding modified problem 373
2. A priori estimates of solutions for the oblique
derivative problem 375
3. Solvability of the oblique derivative problem for
nonlinear complex systems of second order 378
References 384
Index 403
x
|
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| illustrated | Not Illustrated |
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| isbn | 0470213043 |
| language | English |
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| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Wen, Guo-Chun Verfasser aut Boundary value problems for elliptic equations and systems Guo Chun Wen ; Heinrich G. W. Begehr 1. publ. New York u.a. Longman Scientific 1990 XII, 411 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 46 Randwertproblem (DE-588)4048395-2 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptisches Randwertproblem (DE-588)4193399-0 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Randwertproblem (DE-588)4048395-2 s DE-604 Elliptisches Randwertproblem (DE-588)4193399-0 s Begehr, Heinrich G. W. Verfasser aut Pitman monographs and surveys in pure and applied mathematics 46 (DE-604)BV000022446 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002529574&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wen, Guo-Chun Begehr, Heinrich G. W. Boundary value problems for elliptic equations and systems Pitman monographs and surveys in pure and applied mathematics Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4014485-9 (DE-588)4193399-0 |
| title | Boundary value problems for elliptic equations and systems |
| title_auth | Boundary value problems for elliptic equations and systems |
| title_exact_search | Boundary value problems for elliptic equations and systems |
| title_full | Boundary value problems for elliptic equations and systems Guo Chun Wen ; Heinrich G. W. Begehr |
| title_fullStr | Boundary value problems for elliptic equations and systems Guo Chun Wen ; Heinrich G. W. Begehr |
| title_full_unstemmed | Boundary value problems for elliptic equations and systems Guo Chun Wen ; Heinrich G. W. Begehr |
| title_short | Boundary value problems for elliptic equations and systems |
| title_sort | boundary value problems for elliptic equations and systems |
| topic | Randwertproblem (DE-588)4048395-2 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd Elliptisches Randwertproblem (DE-588)4193399-0 gnd |
| topic_facet | Randwertproblem Elliptische Differentialgleichung Elliptisches Randwertproblem |
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