An introduction to maximum principles and symmetry in elliptic problems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2000
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 340 S. graph. Darst. |
| ISBN: | 0521461952 9780521461955 |
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MARC
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| 245 | 1 | 0 | |a An introduction to maximum principles and symmetry in elliptic problems |c L. E. Fraenkel |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2000 | |
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Record in the Search Index
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| adam_text | Contents
Preface page vii
0 Some Notation, Terminology and Basic Calculus 1
1 Introduction 17
1.1 A glimpse of objectives 17
1.2 What are maximum principles? 19
1.3 On reflection in hyperplanes 24
1.4 What is symmetry? 27
1.5 Exercises 32
2 Some Maximum Principles for Elliptic Equations 39
2.1 Linear elliptic operators of order two 39
2.2 The weak maximum principle 41
2.3 The boundary point lemma and the strong maximum principle 50
2.4 A maximum principle for thin sets ft 56
2.5 Steps towards Phragmen Lindelof theory 61
2.6 Comparison functions of Siegel type 72
2.7 Some Phragmen Lindelof theory for subharmonic functions 77
2.8 Exercises 84
3 Symmetry for a Non linear Poisson Equation in a Symmetric
Set £2 87
3.1 The simplest case 87
3.2 A discontinuous non linearity / 93
3.3 Exercises 101
4 Symmetry for the Non linear Poisson Equation in Rs 106
4.1 Statement of the main result 106
4.2 Four lemmas about reflection of t; 111
4.3 Proof of Theorem 4.2 and a corollary 120
v
vi Contents
4.4 Application to some Newtonian potentials 122
4.5 Exercises 133
5 Monotonieity of Positive Solutions in a Bounded Set Q 141
5.1 Prospectus 141
5.2 On the geometry of caps and reflected caps 142
5.3 Monotonieity in Q 153
5.4 A little topology 159
5.5 Exercises 162
Appendix A. On the Newtonian Potential 167
A.I Point sources in R3 167
A.2 The Newtonian potential: first steps 174
A.3 Continuity of the force field Vu 194
A.4 Multipoles and the far field 199
A. 5 Second derivatives of u at points in G 203
A.6 Exercises 213
Appendix B. Rudimentary Facts about Harmonic Functions and
the Poisson Equation 221
B.I Real analytic functions 221
B.2 Smoothness and mean value properties of harmonic
functions 224
B.3 The Kelvin transformation 232
B.4 On the Dirichlet and Neumann problems 235
j B.5 The solution of the Dirichlet problem for a ball 248
B.6 Exercises 262
Appendix C. Construction of the Primary Function of Siegel Type 270
Appendix D. On the Divergence Theorem and Related Matters 279
D.I A first divergence theorem 279
D.2 Extension to some sets with edges and vertices 285
D.3 Interior approximations to the boundary 8Q 293
D.4 Exercises 300
Appendix E. The Edge Point Lemma 305
E.I Preliminaries 305
E.2 Bluntness and ellipticity under co ordinate transformations 309
E.3 Two stages of the edge point lemma 311
Notes on Sources 324
References 332
Index 337
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| any_adam_object | 1 |
| author | Fraenkel, L. Edward 1927-2019 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515.353 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV013434722 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:45:50Z |
| institution | BVB |
| isbn | 0521461952 9780521461955 |
| language | English |
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| physical | X, 340 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Fraenkel, L. Edward 1927-2019 Verfasser (DE-588)143989944 aut An introduction to maximum principles and symmetry in elliptic problems L. E. Fraenkel 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2000 X, 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 128 Symmetrie (DE-588)4058724-1 gnd rswk-swf Maximumprinzip (DE-588)4169165-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s Symmetrie (DE-588)4058724-1 s Maximumprinzip (DE-588)4169165-9 s DE-604 Cambridge tracts in mathematics 128 (DE-604)BV000000001 128 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009168394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fraenkel, L. Edward 1927-2019 An introduction to maximum principles and symmetry in elliptic problems Cambridge tracts in mathematics Symmetrie (DE-588)4058724-1 gnd Maximumprinzip (DE-588)4169165-9 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4169165-9 (DE-588)4014485-9 |
| title | An introduction to maximum principles and symmetry in elliptic problems |
| title_auth | An introduction to maximum principles and symmetry in elliptic problems |
| title_exact_search | An introduction to maximum principles and symmetry in elliptic problems |
| title_full | An introduction to maximum principles and symmetry in elliptic problems L. E. Fraenkel |
| title_fullStr | An introduction to maximum principles and symmetry in elliptic problems L. E. Fraenkel |
| title_full_unstemmed | An introduction to maximum principles and symmetry in elliptic problems L. E. Fraenkel |
| title_short | An introduction to maximum principles and symmetry in elliptic problems |
| title_sort | an introduction to maximum principles and symmetry in elliptic problems |
| topic | Symmetrie (DE-588)4058724-1 gnd Maximumprinzip (DE-588)4169165-9 gnd Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Symmetrie Maximumprinzip Elliptische Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009168394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
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