Hodge Decomposition - A Method for Solving Boundary Value Problems

1995
ISBN: 978-3-540-60016-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1607, 164 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 271 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Schwarz, Günter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Analysis of differential forms.- The hodge decomposition.- Boundary value problems for differential forms.