03607nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001600153072001700169072002300186082001500209100002800224245016500252264008200417300003200499336002600531337002600557338003600583347002400619490005300643505032100696520163101017650001702648650002202665650002402687650003702711650003602748650001702784650002202801650003602823650002402859650002202883700002902905710003402934773002002968776003602988830005303024856004803077978-3-642-32666-0DE-He21320150803155057.0cr nn 008mamaa130107s2013 gw | s |||| 0|eng d a97836423266607 a10.1007/978-3-642-32666-02doi 4aQA404.7-405 7aPBWL2bicssc 7aMAT0330002bisacsh04a515.962231 aMitrea, Irina.eauthor.10aMulti-Layer Potentials and Boundary Problemsh[electronic resource] :bfor Higher-Order Elliptic Systems in Lipschitz Domains /cby Irina Mitrea, Marius Mitrea. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg :bImprint: Springer,c2013. aX, 424 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aLecture Notes in Mathematics,x0075-8434 ;v20630 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. 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. 0aMathematics. 0aFourier analysis. 0aIntegral equations. 0aDifferential equations, partial. 0aPotential theory (Mathematics).14aMathematics.24aPotential Theory.24aPartial Differential Equations.24aIntegral Equations.24aFourier Analysis.1 aMitrea, Marius.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783642326653 0aLecture Notes in Mathematics,x0075-8434 ;v206340uhttp://dx.doi.org/10.1007/978-3-642-32666-0