{"product_id":"9783110482669","title":"The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds","description":"\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 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.\u003cbr\u003eLying 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. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eContents:\u003cbr\u003e\u003c\/b\u003ePreface\u003cbr\u003eIntroduction and Statement of Main Results\u003cbr\u003eGeometric Concepts and Tools\u003cbr\u003eHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains\u003cbr\u003eHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains\u003cbr\u003eDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains\u003cbr\u003eFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains\u003cbr\u003eSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism\u003cbr\u003eAdditional Results and Applications\u003cbr\u003eFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis\u003cbr\u003eBibliography\u003cbr\u003eIndex \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"De Gruyter","offers":[{"title":"Default Title","offer_id":47035281408240,"sku":"9783110482669","price":119.83,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9783110482669_p0.jpg?v=1763718080","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783110482669","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}