On Kato's conjecture and mixed boundary conditions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Göttingen
Sierke Verlag
2015
|
| Ausgabe: | 1. Auflage |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xviii, 360 Seiten Ill., graph. Darst. 25 cm, 700 g |
| ISBN: | 9783868447194 |
Internformat
MARC
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| 100 | 1 | |a Egert, Moritz |d 1988- |e Verfasser |0 (DE-588)1075765188 |4 aut | |
| 245 | 1 | 0 | |a On Kato's conjecture and mixed boundary conditions |c Moritz Egert |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a Göttingen |b Sierke Verlag |c 2015 | |
| 300 | |a xviii, 360 Seiten |b Ill., graph. Darst. |c 25 cm, 700 g | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |b Dissertation |c TU Darmstadt | ||
| 650 | 0 | 7 | |a Kato-Wurzelproblem |0 (DE-588)1081127031 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randbedingung |g Mathematik |0 (DE-588)4725397-6 |2 gnd |9 rswk-swf |
| 653 | |a Fachhochschul-/Hochschulausbildung | ||
| 653 | |a Erwachsenenbildung | ||
| 653 | |a Katos’s conjecture | ||
| 653 | |a mixed boundary conditions | ||
| 653 | |a divergence-form operators | ||
| 653 | |a elliptic boundadary value problems | ||
| 653 | |a Hardy’s inequality | ||
| 653 | |a functional calculus | ||
| 653 | |a DB formalism | ||
| 653 | |a Sobolev extension operators | ||
| 653 | |a fractional Sobolev spaces | ||
| 653 | |a sectorial theory | ||
| 653 | |a Lions problem | ||
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Kato-Wurzelproblem |0 (DE-588)1081127031 |D s |
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Datensatz im Suchindex
| _version_ | 1806333671700955136 |
|---|---|
| adam_text |
CONTENTS
PREFACE V
ZUSAMMENFASSUNG IN DEUTSCHER SPRACHE XV
1 FUNDAMENTALS IN FUNCTION SPACES AND INTERPOLATION THEORY 1
1.1 SPACES OF INTEGRABLE AND DIFFERENTIABLE FUNCTIONS 1
1.1.1 FUNCTION SPACES ON THE WHOLE SPACE 2
1.1.2 FUNCTION SPACES ON DOMAINS 4
1.1.3 VECTOR-VALUED SPACES 7
1.2 A CRASH COURSE IN POTENTIAL THEORY 8
1.2.1 BESSEL CAPACITIES 8
1.2.2 QUASICONTINUOUS FUNCTIONS 10
1.2.3 POTENTIALS OF BOREL MEASURES 12
1.2.4 THICK AND AHLFORS REGULAR SETS 15
1.2.5 SOBOLEV SPACES WITH PARTIALLY VANISHING TRACE . 24
1.2.6 THREE CONCEPTS OF DIMENSION 26
1.3 A GLIMPSE ON INTERPOLATION THEORY 31
1.3.1 ABSTRACT INTERPOLATION THEORY 32
1.3.2 THE K-METHOD OF REAL INTERPOLATION 35
1.3.3 THE COMPLEX INTERPOLATION METHOD 37
1.3.4 INTERPOLATION OF FUNCTION SPACES 40
1.3.5 SNEIBERG'S STABILITY THEOREM 42
2 HARDY'S INEQUALITY 49
2.1 AN ABSTRACT APPROACH TO HARDY'S INEQUALITY 51
2.2 THE STRUCTURE OF SOBOLEV EXTENSION OPERATORS 55
HTTP://D-NB.INFO/1073935655
CONTENTS
2.2.1
DIRICHLET CRACKS CAN BE REMOVED 55
2.2.2 SOBOLEV EXTENDABILITY IS A LOCAL PROPERTY 58
2.2.3 PRESERVATION OF TRACES 61
2.2.4 GEOMETRIC CONDITIONS 66
2.3 POINCARE'S INEQUALITY 72
2.3.1 AN APPROACH VIA POTENTIAL THEORY 73
2.3.2 AN ALTERNATIVE APPROACH 76
2.4 AN INVERSE PROBLEM FOR HARDY'S INEQUALITY 82
2.5 SCALE INVARIANT INTERPOLATION IDENTITIES FOR 91
3 FUNCTIONAL CALCULUS FOR BISECTORIAL AND SECTORIAL OPERATORS 113
3.1 ABSTRACT FUNCTIONAL CALCULI 114
3.2 FUNCTIONAL CALCULI FOR SECTORIAL AND BISECTORIAL OPERATORS . . 117
3.2.1 CONSTRUCTION OF THE FUNCTIONAL CALCULI 120
3.2.2 TRANSFORMED FUNCTIONAL CALCULI 126
3.2.3 A COMPOSITION RULE 134
3.2.4 FRACTIONAL POWERS 136
3.2.5 BOUNDED HOLOMORPHIC SEMIGROUPS 138
3.3 THE H-CALCULUS 141
3.3.1 BOUNDEDNESS OF THE H-CALCULUS 143
3.3.2 M
C
INTOSH APPROXIMATION 145
3.3.3 OPERATORS WITH NON-DENSE RANGE 148
3.3.4 THE SPECTRAL DECOMPOSITION OF BISECTORIAL OPERATORS 149
3.4 QUADRATIC ESTIMATES 154
4 PERTURBED DIRAC TYPE OPERATORS ON AHLFORS REGULAR SETS 165
4.1 QUADRATIC ESTIMATES FOR PERTURBED DIRAC TYPE OPERATORS . . 168
4.2 PROOF OF THEOREM 4.1.11 173
4.2.1 REDUCTION TO FINITE TIME 174
4.2.2 DYADIC DECOMPOSITION 175
4.2.3 OFF-DIAGONAL ESTIMATES 177
4.2.4 SPLITTING THE FINITE TIME INTEGRAL 183
4.2.5 PRINCIPAL PART APPROXIMATION 184
4.2.6 REDUCTION TO A CARLESON MEASURE ESTIMATE 190
4.2.7 THE PROOF OF PROPOSITION 4.2.20 192
4.3 THE REDUCTION THEOREM 197
5 SOLUTION OF KATO'S CONJECTURE FOR MIXED BOUNDARY CONDITIONS 203
II
CONTENTS
5.1 CONTINUOUS SCALE OF SOBOLEV SPACES FOR BOUNDARY CONDITIONS 206
5.1.1 DEFINITION OF THE SPACES HP,
2
206
5.2 UNIVERSAL EXTENSION OPERATORS FOR THE H^-SCALE 211
5.2.1 H
S
'
2
-BOUNDEDNESS OF THE ZERO EXTENSION OPERATOR . . 212
5.2.2 PROOF OF THEOREM 5.2.1 215
5.3 FYACTIONAL HARDY INEQUALITIES FOR PARTIALLY VANISHING TRACE . 220
5.4 INTERPOLATION THEORY 227
5.4.1 PROOF OF (I) 228
5.4.2 PROOF OF THE FIRST EQUALITY IN (II) 229
5.4.3 PROOF OF THE SECOND EQUALITY IN (II) 229
5.4.4 A REMARK ON THE CRITICAL CASE 0 = | 237
5.5 EXTRAPOLATION THEOREM FOR THE LAPLACIAN 239
5.6 THE SOLUTION OF KATO'S CONJECTURE 243
5.6.1 AN EXTENSION TO ELLIPTIC SYSTEMS 247
6 MIXED BOUNDARY VALUE PROBLEMS ON CYLINDRICAL DOMAINS 251
6.1 REFORMULATION AS A FIRST-ORDER SYSTEM 261
6.1.1 LQ
OC
-SOLUTIONS TO THE ELLIPTIC SYSTEM 264
6.1.2 QUADRATIC ESTIMATES FOR THE INFINITESIMAL GENERATOR . 270
6.2 SEMIGROUP SOLUTIONS TO THE FIRST-ORDER SYSTEM 280
6.2.1 OFF-DIAGONAL DECAY 281
6.2.2 THE NON-TANGENTIAL MAXIMAL FUNCTION 286
6.3 THE AUSCHER-AXELSSON REPRESENTATION THEOREMS 306
6.3.1 A DUHAMEL FORMULA FOR THE FIRST-ORDER SYSTEM . . . 307
6.3.2 THE NEUMANN AND REGULARITY PROBLEMS 309
6.3.3 THE DIRICHLET PROBLEM 310
6.4 WELL-POSEDNESS 312
6.4.1 SMALL PERTURBATIONS 316
6.4.2 WELL-POSEDNESS FOR BLOCK AND HERMITEAN MATRICES . 322
6.5 VARIATIONAL SOLUTIONS REVISITED 325
6.5.1 INTERLUDE ON EXTRAPOLATION SPACES 326
6.5.2 IDENTIFICATION OF THE LAX-MILGRAM SEMIGROUP . 329
BIBLIOGRAPHY 331
LIST OF NOTATIONS 345
INDEX 355
III |
| any_adam_object | 1 |
| author | Egert, Moritz 1988- |
| author_GND | (DE-588)1075765188 |
| author_facet | Egert, Moritz 1988- |
| author_role | aut |
| author_sort | Egert, Moritz 1988- |
| author_variant | m e me |
| building | Verbundindex |
| bvnumber | BV043580796 |
| ctrlnum | (OCoLC)951067705 (DE-599)DNB1073935655 |
| dewey-full | 515.7242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7242 |
| dewey-search | 515.7242 |
| dewey-sort | 3515.7242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Auflage |
| format | Thesis Book |
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| spelling | Egert, Moritz 1988- Verfasser (DE-588)1075765188 aut On Kato's conjecture and mixed boundary conditions Moritz Egert 1. Auflage Göttingen Sierke Verlag 2015 xviii, 360 Seiten Ill., graph. Darst. 25 cm, 700 g txt rdacontent n rdamedia nc rdacarrier Dissertation TU Darmstadt Kato-Wurzelproblem (DE-588)1081127031 gnd rswk-swf Randbedingung Mathematik (DE-588)4725397-6 gnd rswk-swf Fachhochschul-/Hochschulausbildung Erwachsenenbildung Katos’s conjecture mixed boundary conditions divergence-form operators elliptic boundadary value problems Hardy’s inequality functional calculus DB formalism Sobolev extension operators fractional Sobolev spaces sectorial theory Lions problem (DE-588)4113937-9 Hochschulschrift gnd-content Kato-Wurzelproblem (DE-588)1081127031 s Randbedingung Mathematik (DE-588)4725397-6 s DE-604 Sierke Verlag (DE-588)1064332609 pbl B:DE-101 application/pdf http://d-nb.info/1073935655/04 Inhaltsverzeichnis X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=5306808&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=028995447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Egert, Moritz 1988- On Kato's conjecture and mixed boundary conditions Kato-Wurzelproblem (DE-588)1081127031 gnd Randbedingung Mathematik (DE-588)4725397-6 gnd |
| subject_GND | (DE-588)1081127031 (DE-588)4725397-6 (DE-588)4113937-9 |
| title | On Kato's conjecture and mixed boundary conditions |
| title_auth | On Kato's conjecture and mixed boundary conditions |
| title_exact_search | On Kato's conjecture and mixed boundary conditions |
| title_full | On Kato's conjecture and mixed boundary conditions Moritz Egert |
| title_fullStr | On Kato's conjecture and mixed boundary conditions Moritz Egert |
| title_full_unstemmed | On Kato's conjecture and mixed boundary conditions Moritz Egert |
| title_short | On Kato's conjecture and mixed boundary conditions |
| title_sort | on kato s conjecture and mixed boundary conditions |
| topic | Kato-Wurzelproblem (DE-588)1081127031 gnd Randbedingung Mathematik (DE-588)4725397-6 gnd |
| topic_facet | Kato-Wurzelproblem Randbedingung Mathematik Hochschulschrift |
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