The Hodge-Laplacian : Boundary Value Problems on Riemannian Manifolds
The Hodge-Laplacian :
Boundary Value Problems on Riemannian Manifolds
by Dorina Mitrea and Irina Mitrea
English | 2016 | ISBN: 3110482665 | 529 Pages | PDF | 2.92 MB
Boundary Value Problems on Riemannian Manifolds
by Dorina Mitrea and Irina Mitrea
English | 2016 | ISBN: 3110482665 | 529 Pages | PDF | 2.92 MB
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 Calderon-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, Poincare, 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.