04267nam 2200577 450 991079873200332120230808195829.03-11-048339-43-11-048438-210.1515/9783110484380(CKB)3710000000887292(MiAaPQ)EBC4707943(DE-B1597)467372(OCoLC)960041744(OCoLC)962087347(DE-B1597)9783110484380(Au-PeEL)EBL4707943(CaPaEBR)ebr11274572(CaONFJC)MIL957926(EXLCZ)99371000000088729220161014h20162016 uy 0engurcnu||||||||rdacontentrdamediardacarrierThe Hodge-Laplacian boundary value problems on Riemannian manifolds /Dorina Mitrea [and three others]Berlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2016.©20161 online resource (528 pages)De Gruyter Studies in Mathematics,0179-0986 ;Volume 643-11-048266-5 Includes bibliographical references and index.Frontmatter -- Preface -- Contents -- 1. Introduction and Statement of Main Results -- 2. Geometric Concepts and Tools -- 3. Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains -- 4. Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains -- 5. Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains -- 6. Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains -- 7. Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism -- 8. Additional Results and Applications -- 9. Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis -- Bibliography -- Index -- BackmatterThe 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 De Gruyter studies in mathematics ;Volume 64.Riemannian manifoldsBoundary value problemsRiemannian manifolds.Boundary value problems.516.3/73SK 540rvkMitrea Dorina, 521700Mitrea Dorina1965-MiAaPQMiAaPQMiAaPQBOOK9910798732003321The Hodge-Laplacian3721641UNINA