MARC Record from harvard_bibliographic_metadata

LEADER: 03896cam a22003853 4500
001 013058947-0
005 20140910154319.0
008 091126s2012 gw a b 001 0 eng d
020 $a9783642104541
020 $a3642104541
035 0 $aocn780248079
035 0 $aocn471802187
040 $aBTCTA$beng$cBTCTA$dYDXCP$dDEBBG$dOHX$dBWX
041 1 $aeng$hfre
050 4 $aQA377$b.N444 2012
100 1 $aNečas, Jindřich.
245 10 $aDirect methods in the theory of elliptic equations /$cJindřich Nečas.
260 $aHeidelberg ;$aNew York :$bSpringer,$cc2012.
300 $axvi, 372 p. :$bill. ;$c25 cm.
490 1 $aSpringer monographs in mathematics
504 $aIncludes bibliographical references (p. 347-364) and indexes.
505 0 $a1. Elementary description of principal results -- 2. The spaces W[supercript k, superscript p] -- 3. Existence, uniqueness and fundamental properties of solutions of boundary value problems -- 4. Regularity of the solution -- 5. Applications of Rellich's equalities and their generalizations to boundary value problems -- 6. Boundary value problems in weighted Sobolev spaces -- 7. Regularity of the solution for non-smooth coefficients and non-regular domains.
520 $aNečas’ 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.
520 $aDue 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.
520 $aThe 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.
650 0 $aDifferential equations, Elliptic.
650 0 $aMathematical analysis.
650 0 $aDifferential equations, partial.
650 0 $aFunctional analysis.
650 0 $aMathematics.
700 1 $aSimader, Christian G.
700 1 $aNečasová, Šárka.
830 0 $aSpringer monographs in mathematics.
988 $a20120112
906 $0OCLC