Coverart for item
The Resource Direct methods in the theory of elliptic equations, Jindřich Nečas ; editorial coordination and preface by Šárka Nečasová ; and a contribution by Christian G. Simader

Direct methods in the theory of elliptic equations, Jindřich Nečas ; editorial coordination and preface by Šárka Nečasová ; and a contribution by Christian G. Simader

Label
Direct methods in the theory of elliptic equations
Title
Direct methods in the theory of elliptic equations
Statement of responsibility
Jindřich Nečas ; editorial coordination and preface by Šárka Nečasová ; and a contribution by Christian G. Simader
Creator
Contributor
Subject
Language
  • eng
  • fre
  • eng
Summary
Nečas' book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas' work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame's system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Nečas, Jindřich
Dewey number
515/.3533
Index
index present
LC call number
QA377
LC item number
.N43 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
NLM call number
Online Book
http://library.link/vocab/relatedWorkOrContributorName
  • Nečasová, Šárka
  • Simader, Christian G
Series statement
Springer monographs in mathematics,
http://library.link/vocab/subjectName
  • Differential equations, Elliptic
  • Mathematics
  • MATHEMATICS
  • MATHEMATICS
  • Differential equations, Elliptic
  • Direkte Methode
  • Elliptische Differentialgleichung
  • Randwertproblem
  • Sobolev-Raum
  • Variationsrechnung
Label
Direct methods in the theory of elliptic equations, Jindřich Nečas ; editorial coordination and preface by Šárka Nečasová ; and a contribution by Christian G. Simader
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 347-364) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Introduction to the problem -- 2. Sobolev spaces -- 3. Exitence, Uniqueness of basic problems -- 4. Regularity of solution -- 5. Applications of Rellich's inequalities and generalization to boundary value problems -- 6. Sobolev spaces with weights and applications to the boundary value problems -- 7. Regularity of solutions in case of irregular domains and elliptic problems with variable coefficients
Control code
757938543
Dimensions
unknown
Extent
1 online resource (xvi, 372 pages).
File format
unknown
Form of item
online
Isbn
9783642104558
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)757938543
Label
Direct methods in the theory of elliptic equations, Jindřich Nečas ; editorial coordination and preface by Šárka Nečasová ; and a contribution by Christian G. Simader
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 347-364) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
1. Introduction to the problem -- 2. Sobolev spaces -- 3. Exitence, Uniqueness of basic problems -- 4. Regularity of solution -- 5. Applications of Rellich's inequalities and generalization to boundary value problems -- 6. Sobolev spaces with weights and applications to the boundary value problems -- 7. Regularity of solutions in case of irregular domains and elliptic problems with variable coefficients
Control code
757938543
Dimensions
unknown
Extent
1 online resource (xvi, 372 pages).
File format
unknown
Form of item
online
Isbn
9783642104558
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)757938543

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