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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)
Resource Information
The item Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 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 selfcontained 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
 Language

 eng
 eng
 Edition
 1st ed. 2012.
 Extent
 1 online resource (383 p.)
 Note
 Originally published in French: Les méthodes directes en théorie des équations elliptiques; Prague, Academia & Paris, Masson et Cie; 1967
 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
 Isbn
 9786613369628
 Label
 Direct Methods in the Theory of Elliptic Equations
 Title
 Direct Methods in the Theory of Elliptic Equations
 Statement of responsibility
 by Jindrich Necas
 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 selfcontained 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
 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
 QA370380
 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)
 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
 10.1007/9783642104558
 Specific material designation
 remote
 System control number

 (CKB)2550000000056317
 (EBL)884773
 (OCoLC)780451854
 (SSID)ssj0000609540
 (PQKBManifestationID)11379229
 (PQKBTitleCode)TC0000609540
 (PQKBWorkID)10620761
 (PQKB)10378792
 (DEHe213)9783642104558
 (MiAaPQ)EBC884773
 (EXLCZ)992550000000056317
 Label
 Direct Methods in the Theory of Elliptic Equations, by Jindrich Necas, (electronic resource)
 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
 10.1007/9783642104558
 Specific material designation
 remote
 System control number

 (CKB)2550000000056317
 (EBL)884773
 (OCoLC)780451854
 (SSID)ssj0000609540
 (PQKBManifestationID)11379229
 (PQKBTitleCode)TC0000609540
 (PQKBWorkID)10620761
 (PQKB)10378792
 (DEHe213)9783642104558
 (MiAaPQ)EBC884773
 (EXLCZ)992550000000056317
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