Hodge decomposition : a method for solving boundary value problems /

Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems....

Full description

Bibliographic Details
Main Author:	Schwarz, Günter, 1959-
Corporate Author:	SpringerLink (Online service)
Format:	eBook
Language:	English
Published:	Berlin ; New York : Springer-Verlag, 1995.
Series:	Lecture notes in mathematics (Springer-Verlag) ; 1607.
Subjects:	Boundary value problems > Numerical solutions. Hodge theory. Decomposition (Mathematics) Problèmes aux limites > Solutions numériques. Hodge, Théorie de. Décomposition (Mathématiques) Randwaardeproblemen. Potentiaaltheorie. Randwertproblem. Numerisches Verfahren. Differentialform. Zerlegung <Mathematik>. Hodge-Theorie. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Ch. 1. Analysis of Differential Forms. 1.1. Manifolds with boundary. 1.2. Differential forms. 1.3. Sobolev spaces. 1.4. Weighted Sobolev spaces. 1.5. Elements of the functional analysis. 1.6. Elliptic boundary value problems
Ch. 2. The Hodge Decomposition. 1.1. Stokes' theorem, the Dirichlet integral and Gaffney's inequalities. 2.2. The Dirichlet and the Neumann potential. 2.3. Regularity of the potential. 2.4. Hodge decomposition on compact [delta]-manifolds. 2.5. Hodge decomposition on exterior domains. 2.6. Elements of de Rham cohomology theory
Appendix: On the smooth deformation of Hilbert space decompositions / J. Wenzelburger
Ch. 3. Boundary Value Problems for Differential Forms. 3.1. The Dirichlet problem for the exterior derivative. 3.2. First order boundary value problems on [actual symbol not reproducible]. 3.3. General inhomogeneous boundary conditions. 3.4. Harmonic fields, harmonic forms and the Poisson equation. 3.5. Vector analysis.