Schwarz, Günter.
Hodge Decomposition—A Method for Solving Boundary Value Problems [electronic resource] / by Günter Schwarz. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1995. - VIII, 164 p. online resource. - Lecture Notes in Mathematics, 1607 0075-8434 ; . - Lecture Notes in Mathematics, 1607 .
Analysis of differential forms -- The hodge decomposition -- Boundary value problems for differential forms.
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.
9783540494034
10.1007/BFb0095978 doi
Mathematics.
Potential theory (Mathematics).
Cell aggregation--Mathematics.
Mathematics.
Potential Theory.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA404.7-405
515.96
Hodge Decomposition—A Method for Solving Boundary Value Problems [electronic resource] / by Günter Schwarz. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1995. - VIII, 164 p. online resource. - Lecture Notes in Mathematics, 1607 0075-8434 ; . - Lecture Notes in Mathematics, 1607 .
Analysis of differential forms -- The hodge decomposition -- Boundary value problems for differential forms.
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.
9783540494034
10.1007/BFb0095978 doi
Mathematics.
Potential theory (Mathematics).
Cell aggregation--Mathematics.
Mathematics.
Potential Theory.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA404.7-405
515.96