The Hodge-Laplacian: boundary value problems on Riemannian manifolds
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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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Berlin ; Boston
De Gruyter
[2025]
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| Ausgabe: | 2nd edition |
| Schriftenreihe: | De Gruyter studies in mathematics
volume 64 |
| Schlagworte: | |
| Online-Zugang: | DE-1043 DE-1046 DE-858 DE-859 DE-860 DE-91 DE-739 Volltext |
| Zusammenfassung: | 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.The 1-st edition of the "Hodge-Laplacian", De Gruyter Studies in Mathematics,Volume 64, 2016, is a trailblazer of its kind, having been written at a time when new results in Geometric Measure Theory have just emerged, or were still being developed. In particular, this monograph is heavily reliant on the bibliographical items. The latter was at the time an unpublished manuscript which eventually developed into the five-volume series "Geometric Harmonic Analysis" published by Springer 2022-2023. The progress registered on this occasion greatly impacts the contents of the "Hodge-Laplacian" and warrants revisiting this monograph in order to significantly sharpen and expand on previous results. This also allows us to provide specific bibliographical references to external work invoked in the new edition.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. |
| Beschreibung: | 1 Online-Ressource (XI, 608 Seiten) |
| ISBN: | 9783111481401 9783111483894 |
| DOI: | 10.1515/9783111481401 |
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| 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.The 1-st edition of the "Hodge-Laplacian", De Gruyter Studies in Mathematics,Volume 64, 2016, is a trailblazer of its kind, having been written at a time when new results in Geometric Measure Theory have just emerged, or were still being developed. In particular, this monograph is heavily reliant on the bibliographical items. The latter was at the time an unpublished manuscript which eventually developed into the five-volume series "Geometric Harmonic Analysis" published by Springer 2022-2023. The progress registered on this occasion greatly impacts the contents of the "Hodge-Laplacian" and warrants revisiting this monograph in order to significantly sharpen and expand on previous results. This also allows us to provide specific bibliographical references to external work invoked in the new edition.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. | ||
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| spelling | Mitrea, Dorina 1965- Verfasser (DE-588)140077642 aut The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor 2nd edition Berlin ; Boston De Gruyter [2025] © 2025 1 Online-Ressource (XI, 608 Seiten) txt rdacontent c rdamedia cr rdacarrier De Gruyter studies in mathematics volume 64 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.The 1-st edition of the "Hodge-Laplacian", De Gruyter Studies in Mathematics,Volume 64, 2016, is a trailblazer of its kind, having been written at a time when new results in Geometric Measure Theory have just emerged, or were still being developed. In particular, this monograph is heavily reliant on the bibliographical items. The latter was at the time an unpublished manuscript which eventually developed into the five-volume series "Geometric Harmonic Analysis" published by Springer 2022-2023. The progress registered on this occasion greatly impacts the contents of the "Hodge-Laplacian" and warrants revisiting this monograph in order to significantly sharpen and expand on previous results. This also allows us to provide specific bibliographical references to external work invoked in the new edition.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. Laplace-Operator Randwertproblem Riemannscher Raum MATHEMATICS / Differential Equations / Partial bisacsh Mitrea, Irina Verfasser (DE-588)1216520623 aut Mitrea, Marius Verfasser (DE-588)1026933625 aut Taylor, Michael Verfasser aut Erscheint auch als Druck-Ausgabe 978-3-11-148098-5 De Gruyter studies in mathematics volume 64 (DE-604)BV044966417 64 https://doi.org/10.1515/9783111481401 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Mitrea, Dorina 1965- Mitrea, Irina Mitrea, Marius Taylor, Michael The Hodge-Laplacian boundary value problems on Riemannian manifolds Laplace-Operator Randwertproblem Riemannscher Raum MATHEMATICS / Differential Equations / Partial bisacsh De Gruyter studies in mathematics |
| 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, Michael Taylor |
| title_fullStr | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor |
| title_full_unstemmed | The Hodge-Laplacian boundary value problems on Riemannian manifolds Dorina Mitrea, Irina Mitrea, Marius Mitrea, 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 | Laplace-Operator Randwertproblem Riemannscher Raum MATHEMATICS / Differential Equations / Partial bisacsh |
| topic_facet | Laplace-Operator Randwertproblem Riemannscher Raum MATHEMATICS / Differential Equations / Partial |
| url | https://doi.org/10.1515/9783111481401 |
| volume_link | (DE-604)BV044966417 |
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