The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds (De Gruy...

Description: The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds (De Gruyter Studies in Mathematics, 64) [Hardcover] Mitrea, Dorina; Mitrea, Irina; Mitrea, Marius and Taylor, Michael Product Overview 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: Preface Introduction and Statement of Main Results Geometric Concepts and Tools Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism Additional Results and Applications Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis Bibliography Index Read more Details Publisher ‏ : ‎ De Gruyter; 1st edition (October 10, 2016) Language ‏ : ‎ English Hardcover ‏ : ‎ 528 pages ISBN-10 ‏ : ‎ 3110482665 ISBN-13 ‏ : ‎ 69 Item Weight ‏ : ‎ 2.26 pounds Dimensions ‏ : ‎ 6.75 x 1.25 x 9.5 inches Best Sellers Rank: #11,842,772 in Books (See Top 100 in Books) #1,502 in Differential Geometry (Books) #4,088 in Geometry #4,910 in Differential Equations (Books) #1,502 in Differential Geometry (Books) #4,088 in Geometry We have been selling used books since 2012, and we've learned that the most important thing is doing good business. Honesty is our policy. Free Shipping We ship worldwide. We have multiple warehouses around the world, so please note the extended handling time on certain listings.

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