Format:
1 online resource (528pages)
ISBN:
9783110484380
,
9783110482669
Series Statement:
De Gruyter studies in mathematics 64
Content:
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
Note:
Description based on online resource; title from PDF title page (publisher's Web site, viewed Sep. 08, 2016)
,
In English
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 978-3-11-048266-9
Language:
English
Subjects:
Mathematics
Keywords:
Laplace-Operator
;
Randwertproblem
;
Riemannscher Raum
DOI:
10.1515/9783110484380
URL:
Volltext
(URL des Erstveröffentlichers)
URL:
Volltext
(lizenzpflichtig)
Author information:
Mitrea, Dorina 1965-
Author information:
Mitrea, Marius
Author information:
Taylor, Michael Eugene 1946-
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