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100   $a20130107d2013      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aMulti-Layer Potentials and Boundary Problems $efor Higher-Order Elliptic Systems in Lipschitz Domains /$fby Irina Mitrea, Marius Mitrea
205   $a1st ed. 2013.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013.
215   $a1 online resource (X, 424 p.) 
225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2063
300   $aBibliographic Level Mode of Issuance: Monograph
311 08$a3-642-32665-X 
320   $aIncludes bibliographical references (pages 405-410) and indexes.
327   $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.
330   $aMany phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach. This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney?Lebesque spaces, Whitney?Besov spaces, Whitney?Sobolev- based Lebesgue spaces, Whitney?Triebel?Lizorkin spaces,Whitney?Sobolev-based Hardy spaces, Whitney?BMO and Whitney?VMO spaces.
410  0$aLecture Notes in Mathematics,$x1617-9692 ;$v2063
606   $aPotential theory (Mathematics)
606   $aDifferential equations
606   $aIntegral equations
606   $aFourier analysis
606   $aPotential Theory
606   $aDifferential Equations
606   $aIntegral Equations
606   $aFourier Analysis
615  0$aPotential theory (Mathematics)
615  0$aDifferential equations.
615  0$aIntegral equations.
615  0$aFourier analysis.
615 14$aPotential Theory.
615 24$aDifferential Equations.
615 24$aIntegral Equations.
615 24$aFourier Analysis.
676   $a515.35
700   $aMitrea$b Irina$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479684
702   $aMitrea$b Marius$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910438149003321
996   $aMulti-Layer Potentials and Boundary Problems$92515934
997   $aUNINA