The Hodge-Laplacian : : Boundary Value Problems on Riemannian Manifolds / / Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor.
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 particu...
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Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2016] ©2016 |
Year of Publication: | 2016 |
Language: | English |
Series: | De Gruyter Studies in Mathematics ,
64 |
Online Access: | |
Physical Description: | 1 online resource (X, 518 p.) |
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100 | 1 | |a Mitrea, Dorina, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 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 ; |a Boston : |b De Gruyter, |c [2016] | |
264 | 4 | |c ©2016 | |
300 | |a 1 online resource (X, 518 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a De Gruyter Studies in Mathematics , |x 0179-0986 ; |v 64 | |
505 | 0 | 0 | |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 |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
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 | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) | |
650 | 0 | |a Boundary value problems. | |
650 | 0 | |a Riemannian manifolds. | |
650 | 4 | |a Laplace-Operator. | |
650 | 4 | |a Randwertproblem. | |
650 | 4 | |a Riemannscher Raum. | |
650 | 7 | |a MATHEMATICS / Geometry / Differential. |2 bisacsh | |
700 | 1 | |a Mitrea, Irina, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
700 | 1 | |a Mitrea, Marius, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
700 | 1 | |a Taylor, Michael, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Plus DeG Package 2016 Part 1 |z 9783110762501 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Plus eBook-Package 2016 |z 9783110701005 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Studies in Mathematics eBook-Package |z 9783110494938 |o ZDB-23-GSM |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2016 |z 9783110485103 |o ZDB-23-DGG |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2016 |z 9783110485288 |o ZDB-23-DMA |
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