000 03765nam a22005295i 4500
001 978-3-642-32666-0
003 DE-He213
005 20140220082853.0
007 cr nn 008mamaa
008 130107s2013 gw | s |||| 0|eng d
020 _a9783642326660
_9978-3-642-32666-0
024 7 _a10.1007/978-3-642-32666-0
_2doi
050 4 _aQA404.7-405
072 7 _aPBWL
_2bicssc
072 7 _aMAT033000
_2bisacsh
082 0 4 _a515.96
_223
100 1 _aMitrea, Irina.
_eauthor.
245 1 0 _aMulti-Layer Potentials and Boundary Problems
_h[electronic resource] :
_bfor Higher-Order Elliptic Systems in Lipschitz Domains /
_cby Irina Mitrea, Marius Mitrea.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aX, 424 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2063
505 0 _a1 Introduction -- 2 Smoothness scales and Caldeón-Zygmund theory in the scalar-valued case -- 3 Function spaces of Whitney arrays -- 4 The double multi-layer potential operator -- 5 The single multi-layer potential operator -- 6 Functional analytic properties of multi-layer potentials and boundary value problems.
520 _aMany phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach. This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney–Lebesque spaces, Whitney–Besov spaces, Whitney–Sobolev- based Lebesgue spaces, Whitney–Triebel–Lizorkin spaces,Whitney–Sobolev-based Hardy spaces, Whitney–BMO and Whitney–VMO spaces.
650 0 _aMathematics.
650 0 _aFourier analysis.
650 0 _aIntegral equations.
650 0 _aDifferential equations, partial.
650 0 _aPotential theory (Mathematics).
650 1 4 _aMathematics.
650 2 4 _aPotential Theory.
650 2 4 _aPartial Differential Equations.
650 2 4 _aIntegral Equations.
650 2 4 _aFourier Analysis.
700 1 _aMitrea, Marius.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642326653
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2063
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-32666-0
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c97272
_d97272