000			03736nam a22004455i 4500
001			978-88-7642-443-4
003			DE-He213
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007			cr nn 008mamaa
008			130730s2012 it | s |||| 0|eng d
020			_a9788876424434 _9978-88-7642-443-4
024	7		_a10.1007/978-88-7642-443-4 _2doi
050		4	_aQA370-380
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.353 _223
100	1		_aGiaquinta, Mariano. _eauthor.
245	1	3	_aAn Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs _h[electronic resource] / _cby Mariano Giaquinta, Luca Martinazzi.
264		1	_aPisa : _bScuola Normale Superiore : _bImprint: Edizioni della Normale, _c2012.
300			_aXIII, 369 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aPublications of the Scuola Normale Superiore
505	0		_a1 Harmonic functions -- 2 Direct methods -- 3 Hilbert space methods -- 4 L2-regularity: the Caccioppoli inequality -- 5 Schauder estimates -- 6 Some real analysis -- 7 Lp-theory -- 8 The regularity problem in the scalar case -- 9 Partial regularity in the vector-valued case -- 10 Harmonic maps -- 11 A survey of minimal graphs.
520			_aThis volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regular problems in the Calculus of Variations always necessarily analytic? 20th problem: does any variational problem have a solution, provided that certain assumptions regarding the given boundary conditions are satisfied, and provided that the notion of a solution is suitably extended? During the last century these two problems have generated a great deal of work, usually referred to as regularity theory, which makes this topic quite relevant in many fields and still very active for research. However, the purpose of this volume, addressed mainly to students, is much more limited. We aim to illustrate only some of the basic ideas and techniques introduced in this context, confining ourselves to important but simple situations and refraining from completeness. In fact some relevant topics are omitted. Topics include: harmonic functions, direct methods, Hilbert space methods and Sobolev spaces, energy estimates, Schauder and Lp-theory both with and without potential theory, including the Calderon-Zygmund theorem, Harnack's and De Giorgi-Moser-Nash theorems in the scalar case and partial regularity theorems in the vector valued case; energy minimizing harmonic maps and minimal graphs in codimension 1 and greater than 1. In this second deeply revised edition we also included the regularity of 2-dimensional weakly harmonic maps, the partial regularity of stationary harmonic maps, and their connections with the case p=1 of the Lp theory, including the celebrated results of Wente and of Coifman-Lions-Meyer-Semmes.
650		0	_aMathematics.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aPartial Differential Equations.
700	1		_aMartinazzi, Luca. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9788876424427
830		0	_aPublications of the Scuola Normale Superiore
856	4	0	_uhttp://dx.doi.org/10.1007/978-88-7642-443-4
912			_aZDB-2-SMA
999			_c104209 _d104209