Hodge decomposition
Subtitle: a method for solving boundary value problems
By: Günter Schwarz.
Series: Lecture notes in mathematics -- 1607
Publisher: Springer
Published: 1995
Place of publication: Berlin; London
Language: eng
Number of pages: 155
Subjects: Boundary value problems -- Numerical solutions.; Hodge theory.; Decomposition (Mathematics)
Description: 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. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity theorems for a wide class of boundary value problems for differential forms and vector fields. The book links aspects of the geometry of manifolds with the theory of partial differential equations. It is intended to be comprehensible for graduate students and mathematicians working in either of these fields.