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020 _a9788876424434
_99788876424434
024 7 _a10.1007/9788876424434
_2doi
035 _avtls000364975
039 9 _a201509030708
_bVLOAD
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040 _aMX-SnUAN
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_cMX-SnUAN
_erda
050 4 _aQA370-380
100 1 _aGiaquinta, Mariano.
_eautor
_9305497
245 1 3 _aAn Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs /
_cby Mariano Giaquinta, Luca Martinazzi.
264 1 _aPisa :
_bScuola Normale Superiore :
_bImprint: Edizioni della Normale,
_c2012.
300 _axiii, 369 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aPublications of the Scuola Normale Superiore
500 _aSpringer eBooks
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.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aMartinazzi, Luca.
_eautor
_9351456
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9788876424427
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-88-7642-443-4
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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