The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds
About this ebook
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
About the author
D. Mitrea and M. Mitrea, Univ. of Missouri, USA;
I. Mitrea, Temple Univ., Philadelphia, USA;
M. Taylor, Univ. of North Carolina, USA.
