000			04199nam a22004575i 4500
001			978-3-642-10455-8
003			DE-He213
005			20140220083255.0
007			cr nn 008mamaa
008			111004s2012 gw | s |||| 0|eng d
020			_a9783642104558 _9978-3-642-10455-8
024	7		_a10.1007/978-3-642-10455-8 _2doi
050		4	_aQA370-380
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.353 _223
100	1		_aNečas, Jindřich. _eauthor.
245	1	0	_aDirect Methods in the Theory of Elliptic Equations _h[electronic resource] / _cby Jindřich Nečas.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012.
300			_aXVI, 372 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringer Monographs in Mathematics, _x1439-7382
505	0		_a1.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.
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. 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.
650		0	_aMathematics.
650		0	_aFunctional analysis.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aPartial Differential Equations.
650	2	4	_aFunctional Analysis.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642104541
830		0	_aSpringer Monographs in Mathematics, _x1439-7382
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-10455-8
912			_aZDB-2-SMA
999			_c101828 _d101828