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Hodge Decomposition - A Method for Solving Boundary Value Problems
Günter Schwarz
出版Springer, 2006-11-14
主題Mathematics / Vector AnalysisMathematics / TopologyMathematics / Probability & Statistics / Stochastic ProcessesMathematics / Mathematical AnalysisMathematics / Geometry / Analytic
ISBN35404940309783540494034
URLhttp://books.google.com.hk/books?id=6-17CwAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.