TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:3710000000887292 ID - ebk01:3710000000887292 LA - eng TI - The Hodge-Laplacian : Boundary Value Problems on Riemannian Manifolds PY - 2016 SN - 9783110484380 AU - Mitrea, Irina. AU - Mitrea, Marius. AU - Taylor, Michael. AB - The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex ER -Download RIS file
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001 | 9783110484380 | ||
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020 | a 9783110484380 | ||
024 | 7 | a 10.1515/9783110484380 2 doi | |
035 | a (DE-B1597)467372 | ||
035 | a (OCoLC)960041744 | ||
040 | a DE-B1597 b eng c DE-B1597 e rda | ||
041 | a eng | ||
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072 | 7 | a MAT012000 2 bisacsh | |
072 | 7 | a MAT012030 2 bisacsh | |
245 | 4 | a The Hodge-Laplacian : b Boundary Value Problems on Riemannian Manifolds / c Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor. | |
264 | 1 | a Berlin ;Boston : b De Gruyter, c [2016] | |
264 | 4 | c ©2016 | |
300 | a 1 online resource (528p.) | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a De Gruyter Studies in Mathematics, x 0179-0986 ; v 64 | ||
505 | t Frontmatter -- t Preface -- t Contents -- t 1. Introduction and Statement of Main Results -- t 2. Geometric Concepts and Tools -- t 3. Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains -- t 4. Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains -- t 5. Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains -- t 6. Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains -- t 7. Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism -- t 8. Additional Results and Applications -- t 9. Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis -- t Bibliography -- t Index -- t Backmatter | ||
520 | a The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex | ||
538 | a Mode of access: Internet via World Wide Web. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016) | ||
650 | 4 | a Laplace-Operator. | |
650 | 4 | a Riemannscher Raum. | |
700 | 1 | a Mitrea, Irina. | |
700 | 1 | a Mitrea, Marius. | |
700 | 1 | a Taylor, Michael. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t DG Studies in Mathematics Backlist eBook Package z 978-3-11-049493-8 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t EBOOK PACKAGE COMPLETE 2016 z 978-3-11-048510-3 o ZDB-23-DGG | |
773 | 8 | i Title is part of eBook package: d De Gruyter t EBOOK PACKAGE Mathematics 2016 z 978-3-11-048528-8 | |
776 | c print z 978-3-11-048266-9 | ||
856 | 4 | u https://doi.org/10.1515/9783110484380 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9783110484380.jpg |
912 | a 978-3-11-048528-8 EBOOK PACKAGE Mathematics 2016 | ||
912 | a 978-3-11-049493-8 DG Studies in Mathematics Backlist eBook Package | ||
912 | a GBV-deGruyter-alles | ||
912 | a GBV-deGruyter-PDA12STME | ||
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912 | a GBV-deGruyter-PDA5EBK | ||
912 | a GBV-deGruyter-PDA7ENG | ||
912 | a ZDB-23-DGG b 2016 |
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