The Hodge-Laplacian: boundary value problems on Riemannian manifolds
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2016]
|
| Schriftenreihe: | De Gruyter Studies in Mathematics
volume 64 |
| Schlagworte: | |
| Online-Zugang: | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110482669&searchTitles=true Inhaltsverzeichnis |
| Beschreibung: | ix, 516 Seiten 24 cm x 17 cm |
| ISBN: | 3110482665 9783110482669 9783110484397 |
Internformat
MARC
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| 100 | 1 | |a Mitrea, Dorina |d 1965- |e Verfasser |0 (DE-588)140077642 |4 aut | |
| 245 | 1 | 0 | |a The Hodge-Laplacian |b boundary value problems on Riemannian manifolds |c Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a ix, 516 Seiten |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Studies in Mathematics |v volume 64 | |
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| 650 | 0 | 7 | |a Riemannscher Raum |0 (DE-588)4128295-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Laplace-Operator |0 (DE-588)4166772-4 |D s |
| 689 | 0 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
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| 700 | 1 | |a Mitrea, Irina |e Verfasser |4 aut | |
| 700 | 1 | |a Mitrea, Marius |e Verfasser |0 (DE-588)1026933625 |4 aut | |
| 700 | 1 | |a Taylor, Michael Eugene |d 1946- |e Verfasser |0 (DE-588)123980119 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804176704836468736 |
|---|---|
| adam_text | CONTENTS
PREFACE
1
1.1
1.2
1.3
1.4
1.5
2
2.1
2.2
2.3
2.4
3
3.1
3.2
3.3
4
4.1
4.2
4.3
5
5.1
5.2
5.3
INTRODUCTION AND STATEMENT OF MAIN RESULTS * 1
FIRST MAIN RESULT: ABSOLUTE AND RELATIVE BOUNDARY CONDITIONS * 3
OTHER PROBLEMS INVOLVING TANGENTIAL AND NORMAL COMPONENTS OF
HARMONIC FORMS * 11
BOUNDARY VALUE PROBLEMS FOR HODGE-DIRAC OPERATORS * 21
DIRICHLET, NEUMANN, TRANSMISSION, POINCARE, AND ROBIN-TYPE BOUNDARY
PROBLEMS * 24
STRUCTURE OF THE MONOGRAPH * 43
GEOMETRIC CONCEPTS AND TOOLS
* 49
DIFFERENTIAL GEOMETRIC PRELIMINARIES * 49
ELEMENTS OF GEOMETRIC MEASURE THEORY * 67
SHARP INTEGRATION BY PARTS FORMULAS FOR DIFFERENTIAL FORMS IN AHLFORS
REGULAR DOMAINS * 91
TANGENTIAL AND NORMAL DIFFERENTIAL FORMS ON AHLFORS REGULAR SETS * 96
HARMONIC LAYER POTENTIALS ASSOCIATED WITH THE HODGE-DE RHAM FORMALISM
ON UR DOMAINS
-----
109
A FUNDAMENTAL SOLUTION FOR THE HODGE-LAPLACIAN * 109
LAYER POTENTIALS FOR THE HODGE-LAPLACIAN
IN THE HODGE-DE RHAM FORMALISM * 117
FREDHOLM THEORY FOR LAYER POTENTIALS
IN THE HODGE-DE RHAM FORMALISM * 128
HARMONIC LAYER POTENTIALS ASSOCIATED WITH THE LEVI-CIVITA CONNECTION
ON UR DOMAINS * 139
THE DEFINITION AND MAPPING PROPERTIES OF THE DOUBLE LAYER
-----
140
THE DOUBLE LAYER ON UR SUBDOMAINS OF SMOOTH MANIFOLDS * 169
COMPACTNESS OF THE DOUBLE LAYER ON REGULAR SKT DOMAINS * 173
DIRICHLET AND NEUMANN BOUNDARY VALUE PROBLEMS FOR THE HODGE-LAPLACIAN
ON REGULAR SKT DOMAINS * 185
FUNCTIONAL ANALYTIC PROPERTIES FOR HARMONIC LAYER POTENTIALS
IN UR DOMAINS * 186
INVERTIBILITY RESULTS FOR LAYER POTENTIALS ASSOCIATED
WITH THE LEVI-CIVITA CONNECTION * 196
SOLVING THE DIRICHLET, NEUMANN, TRANSMISSION, POINCARE, AND ROBIN
BOUNDARY VALUE PROBLEMS * 204
6
6.1
6.2
6.3
7
7.1
7.2
8
8.1
8.2
8.3
8.4
8.5
8.6
9
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
9.11
9.12
FATOU THEOREMS AND INTEGRAL REPRESENTATIONS FOR THE HODGE-LAPLACIAN
ON REGULAR SKT DOMAINS * 231
CONVERGENCE OF FAMILIES OF SINGULAR INTEGRAL OPERATORS * 231
A FATOU THEOREM FOR THE HODGE-LAPLACIAN
IN REGULAR SKT DOMAINS * 250
SPACES OF HARMONIC FIELDS AND GREEN TYPE FORMULAS
-----
261
SOLVABILITY OF BOUNDARY PROBLEMS FOR THE HODGE-LAPLACIAN
IN THE HODGE-DE RHAM FORMALISM * 275
PREPARATORY RESULTS * 275
SOLVABILITY RESULTS * 288
ADDITIONAL RESULTS AND APPLICATIONS * 315
DE RHAM COHOMOLOGY ON REGULAR SKT SURFACES * 315
MAXWELL*S EQUATIONS IN REGULAR SKT DOMAINS * 336
IN REGULAR SKT DOMAINS * 339
FATOU TYPE RESULTS WITH ADDITIONAL CONSTRAINTS
OR REGULARITY CONDITIONS * 347
WEAK TANGENTIAL AND NORMAL TRACES IN REGULAR SKT DOMAINS
WITH FRIEDRICHS PROPERTY * 352
THE HODGE-POISSON KERNEL AND THE HODGE-HARMONIC MEASURE * 367
FURTHER TOOLS FROM DIFFERENTIAL GEOMETRY, HARMONIC ANALYSIS,
GEOMETRIC MEASURE THEORY, FUNCTIONAL ANALYSIS,
PARTIAL DIFFERENTIAL EQUATIONS, AND CLIFFORD ANALYSIS * 371
CONNECTIONS AND COVARIANT DERIVATIVES ON VECTOR BUNDLES * 371
THE EXTENSION OF THE LEVI-CIVITA CONNECTION TO DIFFERENTIAL FORMS * 381
THE BOCHNER-LAPLACIAN AND WEINTZENBOECK*S FORMULA * 386
SOBOLEV SPACES ON BOUNDARIES OF AHLFORS REGULAR DOMAINS:
THE EUCLIDEAN SETTING * 393
SOBOLEV SPACES ON BOUNDARIES OF AHLFORS REGULAR DOMAINS:
THE MANIFOLD SETTING * 408
INTEGRATING BY PARTS ON THE BOUNDARIES
OF AHLFORS REGULAR DOMAINS * 417
A GLOBAL SOBOLEV REGULARITY RESULT * 444
THE PV HARMONIC DOUBLE LAYER ON A UR DOMAIN * 446
CALDERON-ZYGMUND THEORY ON UR DOMAINS ON MANIFOLDS * 451
THE FREDHOLMNESS AND INVERTIBILITY OF ELLIPTIC
DIFFERENTIAL OPERATORS * 474
COMPACT AND CLOSE-TO-COMPACT SINGULAR INTEGRAL OPERATORS * 482
A SHARP DIVERGENCE THEOREM * 490
9.13 CLIFFORD ANALYSIS RUDIMENTS * 493
9.14 SPECTRAL THEORY FOR UNBOUNDED LINEAR OPERATORS
SUBJECT TO CANCELLATIONS * 496
BIBLIOGRAPHY
-----
501
INDEX * 507
|
| any_adam_object | 1 |
| author | Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael Eugene 1946- |
| author_GND | (DE-588)140077642 (DE-588)1026933625 (DE-588)123980119 |
| author_facet | Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael Eugene 1946- |
| author_role | aut aut aut aut |
| author_sort | Mitrea, Dorina 1965- |
| author_variant | d m dm i m im m m mm m e t me met |
| building | Verbundindex |
| bvnumber | BV043837607 |
| classification_rvk | SK 540 |
| classification_tum | MAT 355f |
| ctrlnum | (OCoLC)965125573 (DE-599)DNB1100367489 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043837607 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:36:25Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 3110482665 9783110482669 9783110484397 |
| language | English |
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| physical | ix, 516 Seiten 24 cm x 17 cm |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | De Gruyter |
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| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Mitrea, Dorina 1965- Verfasser (DE-588)140077642 aut The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor Berlin ; Boston De Gruyter [2016] © 2016 ix, 516 Seiten 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics volume 64 Randwertproblem (DE-588)4048395-2 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Laplace-Operator (DE-588)4166772-4 s Randwertproblem (DE-588)4048395-2 s Riemannscher Raum (DE-588)4128295-4 s DE-604 Mitrea, Irina Verfasser aut Mitrea, Marius Verfasser (DE-588)1026933625 aut Taylor, Michael Eugene 1946- Verfasser (DE-588)123980119 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, EPUB 978-3-11-048339-0 Erscheint auch als Online-Ausgabe, PDF 978-3-11-048438-0 De Gruyter Studies in Mathematics volume 64 (DE-604)BV000005407 64 http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110482669&searchTitles=true Verlag DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029248215&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael Eugene 1946- The Hodge-Laplacian boundary value problems on Riemannian manifolds De Gruyter Studies in Mathematics Randwertproblem (DE-588)4048395-2 gnd Laplace-Operator (DE-588)4166772-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4048395-2 (DE-588)4166772-4 (DE-588)4128295-4 |
| title | The Hodge-Laplacian boundary value problems on Riemannian manifolds |
| title_auth | The Hodge-Laplacian boundary value problems on Riemannian manifolds |
| title_exact_search | The Hodge-Laplacian boundary value problems on Riemannian manifolds |
| title_full | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor |
| title_fullStr | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor |
| title_full_unstemmed | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea and Michael Taylor |
| title_short | The Hodge-Laplacian |
| title_sort | the hodge laplacian boundary value problems on riemannian manifolds |
| title_sub | boundary value problems on Riemannian manifolds |
| topic | Randwertproblem (DE-588)4048395-2 gnd Laplace-Operator (DE-588)4166772-4 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Randwertproblem Laplace-Operator Riemannscher Raum |
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