Direct Methods in the Theory of Elliptic Equations (eBook)
XVI, 372 Seiten
Springer Berlin (Verlag)
978-3-642-10455-8 (ISBN)
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.
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.
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 problemhis 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.
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.
Erscheint lt. Verlag | 6.10.2011 |
---|---|
Reihe/Serie | Springer Monographs in Mathematics | Springer Monographs in Mathematics |
Co-Autor | Christian G. Simader |
Übersetzer | Gerard Tronel, Alois Kufner |
Vorwort | Šárka Necasová |
Zusatzinfo | XVI, 372 p. |
Verlagsort | Berlin |
Sprache | englisch |
Original-Titel | Les méthodes directes en théorie des équations elliptiques |
Themenwelt | Mathematik / Informatik ► Mathematik |
Technik | |
Schlagworte | 35J15, 35J45, 35J55 • elliptic equation • Existence • irregular domain • Partial differential equations • regularity • Sobolev Space • weak solution |
ISBN-10 | 3-642-10455-X / 364210455X |
ISBN-13 | 978-3-642-10455-8 / 9783642104558 |
Haben Sie eine Frage zum Produkt? |
Größe: 3,5 MB
DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.
Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.
Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.
Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.
aus dem Bereich