Introduction to partial differential equations
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton Univ. Press
1995
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| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Folland, Gerald B. |d 1947- |e Verfasser |0 (DE-588)137062486 |4 aut | |
| 245 | 1 | 0 | |a Introduction to partial differential equations |c Gerald B. Folland |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1995 | |
| 300 | |a XI, 324 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
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| _version_ | 1816711812805033984 |
| adam_text | CONTENTS
PREFACE ix
Chapter 0
PRELIMINARIES 1
A. Notations and Definitions 1
B. Results from Advanced Calculus 4
C. Convolutions 9
D. The Fourier Transform 14
E. Distributions 17
F. Compact Operators 22
Chapter 1
LOCAL EXISTENCE THEORY 30
A. Basic Concepts 30
B. Real First Order Equations 34
C. The General Cauchy Problem 42
D. The Cauchy Kowalevski Theorem 46
E. Local Solvability: the Lewy Example 56
F. Constant Coefficient Operators: Fundamental Solutions 59
Chapter 2
THE LAPLACE OPERATOR 66
A. Symmetry Properties of the Laplacian 67
B. Basic Properties of Harmonic Functions 68
C. The Fundamental Solution 74
D. The Dirichlet and Neumann Problems 83
E. The Green s Function 85
F. Dirichlet s Principle 88
G. The Dirichlet Problem in a Half Space 91
H. The Dirichlet Problem in a Ball 95
I. More about Harmonic Functions 110
vi Contents
Chapter 3
LAYER POTENTIALS 116
A. The Setup 116
B. Integral Operators 120
C. Double Layer Potentials 123
D. Single Layer Potentials 129
E. Solution of the Problems 134
F. Further Remarks 139
Chapter 4
THE HEAT OPERATOR 142
A. The Gaussian Kernel 143
B. Functions of the Laplacian 149
C. The Heat Equation in Bounded Domains 155
Chapter 5
THE WAVE OPERATOR 159
A. The Cauchy Problem 160
B. Solution of the Cauchy Problem 165
C. The Inhomogeneous Equation 174
D. Fourier Analysis of the Wave Operator 177
E. The Wave Equation in Bounded Domains 183
F. The Radon Transform 185
Chapter 6
THE L2 THEORY OF DERIVATIVES 190
A. Sobolev Spaces on 1 190
B. Further Results on Sobolev Spaces 200
C. Local Regularity of Elliptic Operators 210
D. Constant Coefficient Hypoelliptic Operators 215
E. Sobolev Spaces on Bounded Domains 220
Chapter 7
ELLIPTIC BOUNDARY VALUE PROBLEMS 228
A. Strong Ellipticity 228
B. On Integration by Parts 231
C. Dirichlet Forms and Boundary Conditions 237
D. The Coercive Estimate 242
E. Existence, Uniqueness, and Eigenvalues 248
F. Regularity at the Boundary: the Second Order Case 253
G. Further Results and Techniques 261
H. Epilogue: the Return of the Green s Function 263
Contents vii
Chapter 8
PSEUDODIFFERENTIAL OPERATORS 266
A. Basic Definitions and Properties 266
B. Kernels of Pseudodifferential Operators 271
C. Asymptotic Expansions of Symbols 279
D. Amplitudes, Adjoints, and Products 283
E. Sobolev Estimates 295
F. Elliptic Operators 297
G. Introduction to Microlocal Analysis 304
H. Change of Coordinates 310
BIBLIOGRAPHY 317
INDEX OF SYMBOLS 320
INDEX 322
|
| any_adam_object | 1 |
| author | Folland, Gerald B. 1947- |
| author_GND | (DE-588)137062486 |
| author_facet | Folland, Gerald B. 1947- |
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| author_sort | Folland, Gerald B. 1947- |
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| building | Verbundindex |
| bvnumber | BV011778048 |
| callnumber-first | Q - Science |
| callnumber-label | QA374 F54 1995 |
| callnumber-raw | QA374 F54 1995 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 870 SK 540 |
| classification_tum | MAT 350f |
| ctrlnum | (OCoLC)424103009 (DE-599)BVBBV011778048 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV011778048 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-25T17:16:24Z |
| institution | BVB |
| isbn | 0691043612 9780691043616 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007948818 |
| oclc_num | 424103009 |
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| owner | DE-91G DE-BY-TUM DE-92 DE-355 DE-BY-UBR DE-824 DE-703 DE-706 DE-83 DE-11 DE-20 DE-188 DE-384 DE-19 DE-BY-UBM |
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| physical | XI, 324 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spellingShingle | Folland, Gerald B. 1947- Introduction to partial differential equations Équations aux dérivées partielles Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4044779-0 |
| title | Introduction to partial differential equations |
| title_auth | Introduction to partial differential equations |
| title_exact_search | Introduction to partial differential equations |
| title_full | Introduction to partial differential equations Gerald B. Folland |
| title_fullStr | Introduction to partial differential equations Gerald B. Folland |
| title_full_unstemmed | Introduction to partial differential equations Gerald B. Folland |
| title_short | Introduction to partial differential equations |
| title_sort | introduction to partial differential equations |
| topic | Équations aux dérivées partielles Équations aux dérivées partielles ram Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Équations aux dérivées partielles Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007948818&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT follandgeraldb introductiontopartialdifferentialequations |