The Resource Hodge decomposition : a method for solving boundary value problems, Günter Schwarz
Hodge decomposition : a method for solving boundary value problems, Günter Schwarz
Resource Information
The item Hodge decomposition : a method for solving boundary value problems, Günter Schwarz represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Hodge decomposition : a method for solving boundary value problems, Günter Schwarz represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
- Summary
- 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
- Language
- eng
- Extent
- 1 online resource (155 pages).
- 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
- Isbn
- 9783540494034
- Label
- Hodge decomposition : a method for solving boundary value problems
- Title
- Hodge decomposition
- Title remainder
- a method for solving boundary value problems
- Statement of responsibility
- Günter Schwarz
- Subject
-
- Boundary value problems -- Numerical solutions
- Boundary value problems -- Numerical solutions
- Decomposition (Mathematics)
- Decomposition (Mathematics)
- Decomposition (Mathematics)
- Differentialform
- Hodge theory
- Hodge theory
- Hodge theory
- Hodge-Theorie
- Numerisches Verfahren
- Potentiaaltheorie
- Randwaardeproblemen
- Randwertproblem
- Zerlegung
- Boundary value problems -- Numerical solutions
- Language
- eng
- Summary
- 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
- Cataloging source
- SPLNM
- http://library.link/vocab/creatorDate
- 1959-
- http://library.link/vocab/creatorName
- Schwarz, Günter
- Dewey number
-
- 510 s
- 515/.353
- Index
- index present
- LC call number
-
- QA3
- QA379
- LC item number
- .L28 no. 1607
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- Series statement
- Lecture notes in mathematics,
- Series volume
- 1607
- http://library.link/vocab/subjectName
-
- Boundary value problems
- Hodge theory
- Decomposition (Mathematics)
- Boundary value problems
- Decomposition (Mathematics)
- Hodge theory
- Randwaardeproblemen
- Potentiaaltheorie
- Randwertproblem
- Numerisches Verfahren
- Differentialform
- Zerlegung
- Hodge-Theorie
- Label
- Hodge decomposition : a method for solving boundary value problems, Günter Schwarz
- Bibliography note
- Includes bibliographical references (pages 147-152) and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- 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
- Control code
- 294873438
- Dimensions
- unknown
- Extent
- 1 online resource (155 pages).
- Form of item
- online
- Isbn
- 9783540494034
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
- (OCoLC)294873438
- Label
- Hodge decomposition : a method for solving boundary value problems, Günter Schwarz
- Bibliography note
- Includes bibliographical references (pages 147-152) and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- 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
- Control code
- 294873438
- Dimensions
- unknown
- Extent
- 1 online resource (155 pages).
- Form of item
- online
- Isbn
- 9783540494034
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
- (OCoLC)294873438
Subject
- Boundary value problems -- Numerical solutions
- Boundary value problems -- Numerical solutions
- Decomposition (Mathematics)
- Decomposition (Mathematics)
- Decomposition (Mathematics)
- Differentialform
- Hodge theory
- Hodge theory
- Hodge theory
- Hodge-Theorie
- Numerisches Verfahren
- Potentiaaltheorie
- Randwaardeproblemen
- Randwertproblem
- Zerlegung
- Boundary value problems -- Numerical solutions
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