Nonlinear Second Order Elliptic Equations Involving Measures:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
De Gruyter
2014 [erschienen 2013]
|
| Schriftenreihe: | De Gruyter Series in Nonlinear Analysis and Applications
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIII, 248 S. 240 mm x 170 mm |
| ISBN: | 3110305151 9783110305159 |
Internformat
MARC
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| 245 | 1 | 0 | |a Nonlinear Second Order Elliptic Equations Involving Measures |c Moshe Marcus ; Laurent Véron |
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
PREFACE V
1 LINEAR SECOND ORDER ELLIPTIC EQUATIONS WITH MEASURE DATA 1
1.1 LINEAR BOUNDARY VALUE PROBLEMS WITH L
1
DATA 1
1.2 MEASURE DATA 3
1.3 M-BOUNDARY TRACE 13
1.4 THE HERGLOTZ-DOOB THEOREM 18
1.5 SUBSOLUTIONS, SUPERSOLUTIONS AND KATO'S INEQUALITY 20
1.6 BOUNDARY HARNACK PRINCIPLE 28
1.7 NOTES 32
2 NONLINEAR SECOND ORDER ELLIPTIC EQUATIONS WITH MEASURE DATA 33
2.1 SEMILINEAR PROBLEMS WITH L
1
DATA 33
2.2 SEMILINEAR PROBLEMS WITH BOUNDED MEASURE DATA 36
2.3 SUBCRITICAL NONLINEARITIES 43
2.3.1 WEAK L
P
SPACES 44
2.3.2 CONTINUITY OF G AND IP RELATIVE TO NORM 47
2.3.3 CONTINUITY OF A SUPERPOSITION OPERATOR 48
2.3.4 WEAK CONTINUITY OF SQ 52
2.3.5 WEAK CONTINUITY OF 56
2.4 THE STRUCTURE OF DJL
G
59
2.5 REMARKS ON UNBOUNDED DOMAINS 63
2.6 NOTES 64
3 THE BOUNDARY TRACE AND ASSOCIATED BOUNDARY VALUE PROBLEMS 66
3.1 THE BOUNDARY TRACE 66
3.1.1 MODERATE SOLUTIONS 66
3.1.2 POSITIVE SOLUTIONS 70
3.1.3 UNBOUNDED DOMAINS 78
3.2 MAXIMAL SOLUTIONS 78
3.3 THE BOUNDARY VALUE PROBLEM WITH ROUGH TRACE 81
HTTP://D-NB.INFO/1032800321
XII CONTENTS
3.4 A PROBLEM WITH FADING ABSORPTION 87
3.4.1 THE SIMILARITY TRANSFORMATION AND AN EXTENSION OF THE
KELLER-OSSERMAN ESTIMATE 88
3.4.2 BARRIERS AND MAXIMAL SOLUTIONS 89
3.4.3 THE CRITICAL EXPONENT 94
3.4.4 THE VERY SINGULAR SOLUTION 96
3.5 NOTES 107
4 ISOLATED SINGULARITIES 108
4.1 UNIVERSAL UPPER BOUNDS 108
4.1.1 THE KELLER-OSSERMAN ESTIMATES 108
4.1.2 APPLICATIONS TO MODEL CASES 113
4.2 ISOLATED SINGULARITIES 114
4.2.1 REMOVABLE SINGULARITIES 114
4.2.2 ISOLATED POSITIVE SINGULARITIES 116
4.2.3 ISOLATED SIGNED SINGULARITIES 124
4.3 BOUNDARY SINGULARITIES 130
4.3.1 UPPER BOUNDS 130
4.3.2 THE HALF-SPACE CASE 131
4.3.3 THE CASE OF A GENERAL DOMAIN 138
4.4 BOUNDARY SINGULARITIES WITH FADING ABSORPTION 147
4.4.1 POWER-TYPE DEGENERACY 147
4.4.2 A STRONGLY FADING ABSORPTION 150
4.5 MISCELLANEOUS 156
4.5.1 GENERAL RESULTS OF ISOTROPY 156
4.5.2 ISOLATED SINGULARITIES OF SUPERSOLUTIONS 157
4.6 NOTES AND COMMENTS 159
5 CLASSICAL THEORY OF MAXIMAL AND LARGE SOLUTIONS 162
5.1 MAXIMAL SOLUTIONS 162
5.1.1 GLOBAL CONDITIONS 162
5.1.2 LOCAL CONDITIONS 166
5.2 LARGE SOLUTIONS 166
5.2.1 GENERAL NONLINEARITIES 166
5.2.2 THE POWER AND EXPONENTIAL CASES 171
5.3 UNIQUENESS OF LARGE SOLUTIONS 175
5.3.1 GENERAL UNIQUENESS RESULTS 175
5.3.2 APPLICATIONS TO POWER AND EXPONENTIAL TYPES OF NONLINEARITIES 182
CONTENTS XIII
5.4 EQUATIONS WITH A FORCING TERM 184
5.4.1 MAXIMAL AND MINIMAL LARGE SOLUTIONS 184
5.4.2 UNIQUENESS 188
5.5 NOTES AND COMMENTS 192
6 FURTHER RESULTS ON SINGULARITIES AND LARGE SOLUTIONS 195
6.1 SINGULARITIES 195
6.1.1 INTERNAL SINGULARITIES 195
6.1.2 BOUNDARY SINGULARITIES 205
6.2 SYMMETRIES OF LARGE SOLUTIONS 217
6.3 SHARP BLOW UP RATE OF LARGE SOLUTIONS 226
6.3.1 ESTIMATES IN AN ANNULUS 227
6.3.2 CURVATURE SECONDARY EFFECTS 231
6.4 NOTES AND COMMENTS 235
BIBLIOGRAPHY 239
INDEX 247 |
| any_adam_object | 1 |
| author | Marcus, Moshe Véron, Laurent |
| author_GND | (DE-588)1044764635 (DE-588)1044764732 |
| author_facet | Marcus, Moshe Véron, Laurent |
| author_role | aut aut |
| author_sort | Marcus, Moshe |
| author_variant | m m mm l v lv |
| building | Verbundindex |
| bvnumber | BV041447198 |
| classification_rvk | SK 540 |
| ctrlnum | (OCoLC)864646635 (DE-599)DNB1032800321 |
| dewey-full | 515.3533 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.3533 |
| dewey-search | 515.3533 |
| dewey-sort | 3515.3533 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041447198 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-10T01:02:57Z |
| institution | BVB |
| isbn | 3110305151 9783110305159 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026893837 |
| oclc_num | 864646635 |
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| owner_facet | DE-19 DE-BY-UBM DE-20 |
| physical | XIII, 248 S. 240 mm x 170 mm |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Series in Nonlinear Analysis and Applications |
| series2 | De Gruyter Series in Nonlinear Analysis and Applications |
| spelling | Marcus, Moshe Verfasser (DE-588)1044764635 aut Nonlinear Second Order Elliptic Equations Involving Measures Moshe Marcus ; Laurent Véron Berlin [u.a.] De Gruyter 2014 [erschienen 2013] XIII, 248 S. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier De Gruyter Series in Nonlinear Analysis and Applications 21 Ordnung 2 (DE-588)4350619-7 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd rswk-swf Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 s Ordnung 2 (DE-588)4350619-7 s DE-604 Véron, Laurent Verfasser (DE-588)1044764732 aut Erscheint auch als Online-Ausgabe 978-3-11-030531-9 De Gruyter Series in Nonlinear Analysis and Applications 21 (DE-604)BV005530011 21 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4284870&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=026893837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marcus, Moshe Véron, Laurent Nonlinear Second Order Elliptic Equations Involving Measures De Gruyter Series in Nonlinear Analysis and Applications Ordnung 2 (DE-588)4350619-7 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| subject_GND | (DE-588)4350619-7 (DE-588)4310554-3 |
| title | Nonlinear Second Order Elliptic Equations Involving Measures |
| title_auth | Nonlinear Second Order Elliptic Equations Involving Measures |
| title_exact_search | Nonlinear Second Order Elliptic Equations Involving Measures |
| title_full | Nonlinear Second Order Elliptic Equations Involving Measures Moshe Marcus ; Laurent Véron |
| title_fullStr | Nonlinear Second Order Elliptic Equations Involving Measures Moshe Marcus ; Laurent Véron |
| title_full_unstemmed | Nonlinear Second Order Elliptic Equations Involving Measures Moshe Marcus ; Laurent Véron |
| title_short | Nonlinear Second Order Elliptic Equations Involving Measures |
| title_sort | nonlinear second order elliptic equations involving measures |
| topic | Ordnung 2 (DE-588)4350619-7 gnd Nichtlineare elliptische Differentialgleichung (DE-588)4310554-3 gnd |
| topic_facet | Ordnung 2 Nichtlineare elliptische Differentialgleichung |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4284870&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=026893837&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005530011 |
| work_keys_str_mv | AT marcusmoshe nonlinearsecondorderellipticequationsinvolvingmeasures AT veronlaurent nonlinearsecondorderellipticequationsinvolvingmeasures |