The Resource Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource)

Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource)

Label
Direct Methods in the Theory of Elliptic Equations
Title
Direct Methods in the Theory of Elliptic Equations
Statement of responsibility
by Jindrich Necas
Creator
Author
Author
Subject
Language
  • eng
  • 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
Is Subseries of
http://library.link/vocab/creatorName
Necas, Jindrich
Dewey number
  • 515.3533
  • 515/.3533
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
VRh9ESKuHyc
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Functional analysis
  • Partial Differential Equations
  • Functional Analysis
Label
Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource)
Instantiates
Publication
Note
Originally published in French: Les méthodes directes en théorie des équations elliptiques; Prague, Academia & Paris, Masson et Cie; 1967
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2012.
Extent
1 online resource (383 p.)
Form of item
online
Isbn
9786613369628
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-642-10455-8
Specific material designation
remote
System control number
  • (CKB)2550000000056317
  • (EBL)884773
  • (OCoLC)780451854
  • (SSID)ssj0000609540
  • (PQKBManifestationID)11379229
  • (PQKBTitleCode)TC0000609540
  • (PQKBWorkID)10620761
  • (PQKB)10378792
  • (DE-He213)978-3-642-10455-8
  • (MiAaPQ)EBC884773
  • (EXLCZ)992550000000056317
Label
Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource)
Publication
Note
Originally published in French: Les méthodes directes en théorie des équations elliptiques; Prague, Academia & Paris, Masson et Cie; 1967
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
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
Dimensions
unknown
Edition
1st ed. 2012.
Extent
1 online resource (383 p.)
Form of item
online
Isbn
9786613369628
Media category
computer
Media type code
  • c
Other control number
10.1007/978-3-642-10455-8
Specific material designation
remote
System control number
  • (CKB)2550000000056317
  • (EBL)884773
  • (OCoLC)780451854
  • (SSID)ssj0000609540
  • (PQKBManifestationID)11379229
  • (PQKBTitleCode)TC0000609540
  • (PQKBWorkID)10620761
  • (PQKB)10378792
  • (DE-He213)978-3-642-10455-8
  • (MiAaPQ)EBC884773
  • (EXLCZ)992550000000056317

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