Elliptic partial differential equations: existence and regularity of distributional solutions
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
De Gruyter
2014
|
| Schriftenreihe: | De Gruyter Studies in Mathematics
55 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | IX, 192 S. |
| ISBN: | 9783110315400 9783110315431 |
Internformat
MARC
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| 100 | 1 | |a Boccardo, Lucio |e Verfasser |0 (DE-588)1046952323 |4 aut | |
| 245 | 1 | 0 | |a Elliptic partial differential equations |b existence and regularity of distributional solutions |c Lucio Boccardo ; Gisella Croce |
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2014 | |
| 300 | |a IX, 192 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1806326153085976576 |
|---|---|
| adam_text |
CONTENTS
NOTATIONS X
1 INTRODUCTION 1
PART I
2 SOME FIXED POINT THEOREMS 5
2.1 INTRODUCTION 5
2.2 BANACH-CACCIOPPOLI THEOREM 5
2.3 BROUWER'S THEOREM 6
2.4 SCHAUDER'S THEOREM*10
3 PRELIMINARIES OF REAL ANALYSIS * 13
3.1 INTRODUCTION 13
3.2 NEMITSKI'S COMPOSITION THEOREM* 13
3.3 MARCINKIEWICZ SPACES 18
3.4 APPENDIX 22
4 LINEAR AND SEMILINEAR ELLIPTIC EQUATIONS 24
4.1 INTRODUCTION 24
4.2 THE LAX-MILGRAM AND STAMPACCHIA'S THEOREMS
4.3 LINEAR EQUATIONS 27
4.4 SOME SEMILINEAR MONOTONE EQUATIONS 28
4.5 SUB AND SUPERSOLUTIONS METHOD 31
4.6 APPENDIX 34
5 NONLINEAR ELLIPTIC EQUATIONS 37
5.1 INTRODUCTION 37
5.2 SURJECTIVITY THEOREM 37
5.3 THE LERAY-LIONS EXISTENCE THEOREM 40
6 SUMMABILITY OF THE SOLUTIONS 47
6.1 INTRODUCTION 47
6.2 PRELIMINARIES 48
6.3 SOURCES IN LEBESGUE SPACES 51
6.4 SOURCES IN MARCINKIEWICZ SPACES 56
6.5 SOURCES IN DIVERGENCE FORM 58
HTTP://D-NB.INFO/1036475042
VIII *
CONTENTS
7 H
2
REGULARITY FOR LINEAR PROBLEMS 61
7.1 INTRODUCTION 61
7.2 PRELIMINARIES 61
7.3 H
2
(D.) REGULARITY OF THE SOLUTIONS 63
8 SPECTRAL ANALYSIS FOR LINEAR OPERATORS 67
8.1 INTRODUCTION 67
8.2 EIGENVALUES OF LINEAR ELLIPTIC OPERATORS 67
8.3 APPLICATIONS TO SOME SEMILINEAR EQUATIONS 74
8.4 APPENDIX 82
9 CALCULUS OF VARIATIONS AND EULER'S EQUATION * 84
9.1 INTRODUCTION 84
9.2 DIRECT METHODS IN THE CALCULUS OF VARIATIONS 84
9.3 EULER EQUATION 86
9.4 SUMMABILITY OF MINIMIZERS OF INTEGRAL FUNCTIONALS 90
9.5 THE EKELAND VARIATIONAL PRINCIPLE 95
9.6 APPENDIX 102
PART II
10 NATURAL GROWTH PROBLEMS 105
10.1 INTRODUCTION 105
10.2 A PROBLEM WITH BOUNDED SOLUTIONS 106
10.3 A PROBLEM WITH UNBOUNDED SOLUTIONS * 112
11 PROBLEMS WITH LOW SUMMABLE SOURCES * 121
11.1 INTRODUCTION 121
11.2 A PRIORI ESTIMATES 123
11.3 DISTRIBUTIONAL SOLUTIONS 130
11.4 THE LINEAR CASE: A DIFFERENT PROOF 130
11.5 ENTROPY SOLUTIONS 132
11.6 A COMPARISON BETWEEN ENTROPY SOLUTIONS AND
DISTRIBUTIONAL SOLUTIONS 137
11.7 MEASURE SOURCES 138
11.8 THE REGULARIZING EFFECTS OF A LOWER ORDER TERM* 140
11.9 T-MINIMA 143
11.10 APPENDIX 148
12 UNIQUENESS 150
12.1 INTRODUCTION 150
12.2 MONOTONE ELLIPTIC OPERATORS 150
12.3 A NONMONOTONE ELLIPTIC OPERATOR* 152
12.4 A UNIQUENESS RESULT FOR MEASURE SOURCES 154
13 A PROBLEM WITH POLYNOMIAL GROWTH * 157
13.1 INTRODUCTION 157
13.2 EXISTENCE RESULTS 158
14 A PROBLEM WITH DEGENERATE COERCIVITY 166
14.1 INTRODUCTION 166
14.2 THE CASE 0 8 1 167
14.3 THE CASE 9 1: EXISTENCE AND NONEXISTENCE* 172
14.4 THE REGULARIZING EFFECTS OF A LOWER ORDER TERM 175
BIBLIOGRAPHY 187
INDEX 191 |
| any_adam_object | 1 |
| author | Boccardo, Lucio Croce, Gisella |
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| author_facet | Boccardo, Lucio Croce, Gisella |
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| bvnumber | BV041370104 |
| classification_rvk | SK 560 |
| ctrlnum | (OCoLC)862834201 (DE-599)DNB1036475042 |
| dewey-full | 510 515.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515.3533 |
| dewey-search | 510 515.3533 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-08-03T01:00:59Z |
| institution | BVB |
| isbn | 9783110315400 9783110315431 |
| language | English |
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| physical | IX, 192 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Boccardo, Lucio Verfasser (DE-588)1046952323 aut Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce Berlin [u.a.] De Gruyter 2014 IX, 192 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics 55 Elliptische Differentialgleichung (DE-588)4014485-9 gnd rswk-swf Elliptische Differentialgleichung (DE-588)4014485-9 s DE-604 Croce, Gisella Verfasser (DE-588)1046952730 aut Erscheint auch als Online-Ausgabe 978-3-11-031542-4 De Gruyter Studies in Mathematics 55 (DE-604)BV000005407 55 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4372578&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026818273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Boccardo, Lucio Croce, Gisella Elliptic partial differential equations existence and regularity of distributional solutions De Gruyter Studies in Mathematics Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| subject_GND | (DE-588)4014485-9 |
| title | Elliptic partial differential equations existence and regularity of distributional solutions |
| title_auth | Elliptic partial differential equations existence and regularity of distributional solutions |
| title_exact_search | Elliptic partial differential equations existence and regularity of distributional solutions |
| title_full | Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce |
| title_fullStr | Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce |
| title_full_unstemmed | Elliptic partial differential equations existence and regularity of distributional solutions Lucio Boccardo ; Gisella Croce |
| title_short | Elliptic partial differential equations |
| title_sort | elliptic partial differential equations existence and regularity of distributional solutions |
| title_sub | existence and regularity of distributional solutions |
| topic | Elliptische Differentialgleichung (DE-588)4014485-9 gnd |
| topic_facet | Elliptische Differentialgleichung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4372578&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026818273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
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