{"product_id":"the-hodge-laplacian-boundary-value-problems-on-riemannian-manifolds-9783110482669","title":"The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds","description":"\u003cp\u003e • Author(s): Dorina Mitrea | Irina Mitrea | Marius Mitrea\u003cbr\u003e • Publisher: de Gruyter\u003cbr\u003e • Publisher Imprint: de Gruyter\u003cbr\u003e • BISAC: Geometry - Differential\u003c\/p\u003e\u003cp\u003eThe 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 Calder�n-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, Poincar�, 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\u003c\/p\u003e","brand":"de Gruyter","offers":[{"title":"Hardcover","offer_id":47890295554199,"sku":"9783110482669","price":16630.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783110482669.webp?v=1781179415","url":"https:\/\/atlanticbooks.com\/products\/the-hodge-laplacian-boundary-value-problems-on-riemannian-manifolds-9783110482669","provider":"Atlantic Books","version":"1.0","type":"link"}