Articles liés à Direct Methods in the Theory of Elliptic Equations
Synopsis
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.
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À propos de l?auteur
Jindrich Necas, Professor Emeritus of the Charles University in Prague, Distinguished Researcher Professor at the University of Northern Illinois, DeKalb, Doctor Honoris Causa at the Technical University of Dresden, a leading Czech mathematician and a world-class researcher in the field of partial differential equations. Author or coauthor of 12 monographs, 7 textbooks, and 185 research papers. High points of his research include
- his contribution to boundary regularity theory for linear systems
- his contributions to regularity theory of variational integrals, such as his 1977 solution of a long-standing question directly to Hilbert's 19th problem
- his contributions to mathematical theory of the Navier-stokes equations, including his 1995 solution of an important problem raised in a classical 1934 paper by J. Leray.
In 1998 he was awarded the Order of Merit of the Czech Republic by President Václav Havel.
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Direct Methods in the Theory of Elliptic Equations
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Direct Methods in the Theory of Elliptic Equations (Hardcover)
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Hardcover. Etat : new. Hardcover. Necas 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 Necas 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, Lames 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 Lamesystem 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. Necas 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783642104541
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Direct Methods in the Theory of Elliptic Equations (Springer Monographs in Mathematics)
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Direct Methods in the Theory of Elliptic Equations
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Direct Methods in the Theory of Elliptic Equations (Springer Monographs in Mathematics)
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Direct Methods in the Theory of Elliptic Equations
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ISBN 13 : 9783642104541
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Necas' 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 Necas' 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. 388 pp. Englisch. N° de réf. du vendeur 9783642104541
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Direct Methods in the Theory of Elliptic Equations
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. A standard reference for the mathematical theory of linear elliptic equations and systemsOriginally published 1967 in FrenchAny researcher using the theory of elliptic systems will benefit from this bookA standard reference for t. N° de réf. du vendeur 5049245
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Direct Methods in the Theory of Elliptic Equations
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Etat : New. This text covers the mathematical theory of linear elliptic equations and systems and the related function spaces framework. It provides an introduction to the modern theory of partial differential equations, the theory of weak solutions and related topics. Translator(s): Tronel, Gerard; Kufner, Alois. Series: Springer Monographs in Mathematics. Num Pages: 388 pages, biography. BIC Classification: PBKF; PBKJ. Category: (P) Professional & Vocational. Dimension: 241 x 163 x 26. Weight in Grams: 712. . 2010. 1st ed. Corr. 3rd printing 2012. Hardback. . . . . N° de réf. du vendeur V9783642104541
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Direct Methods in the Theory of Elliptic Equations
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Direct Methods in the Theory of Elliptic Equations
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Buch. Etat : Neu. Neuware -Ne¿as¿ 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 Ne¿as¿ 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 Lamesystem 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 388 pp. Englisch. N° de réf. du vendeur 9783642104541
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