Partial differential equations and complex analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
1992
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| Series: | Studies in advanced mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 297 S. graph. Darst. |
| ISBN: | 0849371554 |
Staff View
MARC
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| 245 | 1 | 0 | |a Partial differential equations and complex analysis |c Steven G. Krantz |
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 The Dirichlet Problem in the Complex Plane 1
1.1 A Little Notation 1
1.2 The Dirichlet Problem 2
1.3 Lipschitz Spaces 7
1.4 Boundary Regularity for the Dirichlet Problem for the
Laplacian on the Unit Disc 10
1.5 Regularity of the Dirichlet Problem on a Smoothly
Bounded Domain and Conformal Mapping 20
2 Review of Fourier Analysis 26
2.1 The Fourier Transform 26
2.2 Schwartz Distributions 36
2.3 Convolution and Friedrichs Mollifiers 43
2.4 The Paley Wiener Theorem 48
3 Pseudodifferential Operators 52
3.1 Introduction to Pseudodifferential Operators 52
3.2 A Formal Treatment of Pseudodifferential Operators 56
3.3 The Calculus of Pseudodifferential Operators 65
4 Elliptic Operators 76
4.1 Some Fundamental Properties of Partial Differential
Operators 76
vii
VHJ
4.2 Regularity for Elliptic Operators 81
4.3 Change of Coordinates 87 i
4.4 Restriction Theorems for Sobolev Spaces 89
i
i
5 Elliptic Boundary Value Problems 95 I
5.1 The Constant Coefficient Case 95
5.2 Well Posedness 99
5.3 Remarks on the Solution of the Boundary Value Problem
in the Constant Coefficient Case 108
5.4 Solution of the Boundary Value Problem in the Variable j
Coefficient Case 109 j
5.5 Solution of the Boundary Value Problem Using I
Pseudodifferential Operators 115 !
5.6 Remarks on the Dirichlet Problem on an Arbitrary j
Domain, and a Return to Conformal Mapping 123
5.7 A Coda on the Neumann Problem 126
O A Degenerate Elliptic Boundary Value Problem 128
6.1 Introductory Remarks 128
6.2 The Bergman Kernel 131
6.3 The Szego and Poisson Szego Kernels 138
6.4 The Bergman Metric 143
6.5 The Dirichlet Problem for the Invariant Laplacian
on the Ball 148
6.6 Spherical Harmonics 154
6.7 Advanced Topics in the Theory of Spherical Harmonics:
the Zonal Harmonics 160
6.8 Spherical Harmonics in the Complex Domain and
Applications 172
7 The d Neumann Problem 184
7.1 Introduction to Hermitian Analysis 185
7.2 The Formalism of the 5 Problem 189
7.3 Formulation of the ^ Neumann Problem 196
7.4 The Main Estimate 201
7.5 Special Boundary Charts, Finite Differences, and Other
Technical Matters 208
7.6 First Steps in the Proof of the Main Estimate 218
7.7 Estimates in the Sobolev 1/2 Norm 224
7.8 Conclusion of the Proof of the Main Estimate 234
7.9 The Solution of the 0 Neumann Problem 242
ix
8 Applications of the B Neumann Problem 252
8.1 An Application to the Bergman Projection 252
8.2 Smoothness to the Boundary of Biholomorphic Mappings 256
8.3 Other Applications of 3 Techniques 263
9 The Local Solvability Issue and a Look Back 269
9.1 Some Remarks about Local Solvabilitiy 269
9.2 The Szego Projection and Local Solvability 270
9.3 The Hodge Theory for the Tangential Cauchy Riemann
Complex 274
9.4 Commutators, Integrability, and Local Solvability 277
Table of Notation 283
Bibliography 287
Index 295
|
| any_adam_object | 1 |
| author | Krantz, Steven G. 1951- |
| author_GND | (DE-588)130535907 |
| author_facet | Krantz, Steven G. 1951- |
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| author_variant | s g k sg sgk |
| building | Verbundindex |
| bvnumber | BV006146376 |
| classification_rvk | SK 540 SK 750 SK 780 SK 620 |
| classification_tum | MAT 474f MAT 300f MAT 320f MAT 350f |
| ctrlnum | (OCoLC)260153063 (DE-599)BVBBV006146376 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T16:41:03Z |
| institution | BVB |
| isbn | 0849371554 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003885946 |
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| physical | XII, 297 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Studies in advanced mathematics |
| spelling | Krantz, Steven G. 1951- Verfasser (DE-588)130535907 aut Partial differential equations and complex analysis Steven G. Krantz Boca Raton, Fla. [u.a.] CRC Press 1992 XII, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Komplexe Variable (DE-588)4164905-9 s Funktionentheorie (DE-588)4018935-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003885946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krantz, Steven G. 1951- Partial differential equations and complex analysis Funktionentheorie (DE-588)4018935-1 gnd Komplexe Variable (DE-588)4164905-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018935-1 (DE-588)4164905-9 (DE-588)4044779-0 (DE-588)4018916-8 |
| title | Partial differential equations and complex analysis |
| title_auth | Partial differential equations and complex analysis |
| title_exact_search | Partial differential equations and complex analysis |
| title_full | Partial differential equations and complex analysis Steven G. Krantz |
| title_fullStr | Partial differential equations and complex analysis Steven G. Krantz |
| title_full_unstemmed | Partial differential equations and complex analysis Steven G. Krantz |
| title_short | Partial differential equations and complex analysis |
| title_sort | partial differential equations and complex analysis |
| topic | Funktionentheorie (DE-588)4018935-1 gnd Komplexe Variable (DE-588)4164905-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionentheorie Komplexe Variable Partielle Differentialgleichung Funktionalanalysis |
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