Abstract methods in partial differential equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Harper & Row
1969
|
| Series: | Harper's series in modern mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 374 S. |
Staff View
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| 245 | 1 | 0 | |a Abstract methods in partial differential equations |c Robert W. Carroll |
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Record in the Search Index
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CONTENTS
Introduction vii
CHAPTER 1. FUNCTIONAL ANALYSIS AND DISTRIBUTIONS 1
1. Introduction 1
2. Locally Convex Spaces 1
3. The Space® 7
4. Differentiation in Q and Examples 9
5. Differentiation in® (R1) 14
6. The Spaces S, V, T, 9 and the Fourier Transform 16
7. Tensor Products and Convolution 20
8. Topologies in and S —Duality Theory 28
9. Regularization 37
10. Some Functional Analysis 38
11. Vector-Valued Distributions and Integration 45
CHAPTER 2. ELLIPTIC THEORY 57
1. Introduction 57
2. Unbounded Operators—Sobolev Spaces 58
3. Forms and Operators 62
4. Some Linear Elliptic Results Following Lions-Magenes 67
5. Monotonicity—Hemi- and Demicontinuity 73
6. Nonlinear Elliptic Theory Following F. Browder 80
7. Some Remarks on Compactness 86
8. The Calculus of Variations Following F. Browder 89
9. Variational Methods and Monotone Operators 97
CHAPTER 3. EVOLUTION EQUATIONS I 103
1. Introduction 103
2. Examples from Physics 103
3. Survey of Hyperbolic and Parabolic Ideas 116
4. Vector-Valued Ordinary Differential Equations 123
5. Evolution Operators and Integral Equations 134
6. Monotonicity and Integral Equations of Evolution Type 144
v
vi Contents
CHAPTER 4. EVOLUTION EQUATIONS II (WEAK PROBLEMS) 156
1. Introduction 156
2. Some Functional Analysis—Semigroups 156
3. Weak Linear Problems—Existence Theory 167
4. Some Functional Analysis—Schwartz Kernels—Operators with Closed Range 177
5. Uniqueness and Regularity for Weak Problems with Variable Domains 183
6. More on Uniqueness and Regularity 199
CHAPTER 5. EVOLUTION EQUATIONS III (STRONG PROBLEMS) 210
1. Introduction 210
2. Abstract Strong Problems 210
3. Interacting Spectra and Interpolation 223
4. Evolution Operators Following Kato-Tanabe 229
5. Nonlinear Evolution Equations 246
6. Spectral Methods for Higher-Order Equations 255
CHAPTER 6. GLOBAL ANALYSIS 269
1. Introduction 269
2. Manifolds 270
3. Tensors and Forms 276
4. Vector Bundles 283
5. Differential Operators in Vector Bundles 295
6. Elliptic Operators and Index Theory (Sketch) 309
Appendix I. Some Topology and Fixed-Point Theory 315
Appendix II. Banach Algebras, Analytic Functional Calculus, Fractional Powers
of Operators, and Interpolation Theory 322
References 342
Index 369
|
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| indexdate | 2024-07-09T15:49:00Z |
| institution | BVB |
| language | English |
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| physical | IX, 374 S. |
| psigel | HUB-ZB011200712 |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Harper & Row |
| record_format | marc |
| series2 | Harper's series in modern mathematics |
| spelling | Carroll, Robert Wayne 1930- Verfasser (DE-588)123067669 aut Abstract methods in partial differential equations Robert W. Carroll New York [u.a.] Harper & Row 1969 IX, 374 S. txt rdacontent n rdamedia nc rdacarrier Harper's series in modern mathematics Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Équations aux dérivées partielles ram Differential equations, Partial Methode (DE-588)4038971-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Methode (DE-588)4038971-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carroll, Robert Wayne 1930- Abstract methods in partial differential equations Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Équations aux dérivées partielles ram Differential equations, Partial Methode (DE-588)4038971-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4038971-6 (DE-588)4044779-0 |
| title | Abstract methods in partial differential equations |
| title_auth | Abstract methods in partial differential equations |
| title_exact_search | Abstract methods in partial differential equations |
| title_full | Abstract methods in partial differential equations Robert W. Carroll |
| title_fullStr | Abstract methods in partial differential equations Robert W. Carroll |
| title_full_unstemmed | Abstract methods in partial differential equations Robert W. Carroll |
| title_short | Abstract methods in partial differential equations |
| title_sort | abstract methods in partial differential equations |
| topic | Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Équations aux dérivées partielles ram Differential equations, Partial Methode (DE-588)4038971-6 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Partiële differentiaalvergelijkingen Équations aux dérivées partielles Differential equations, Partial Methode Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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