Multilayer Potentials And Boundary Problems: For Higherorder Elliptic Systems In Lipschitz Domains (Lecture Notes In Mathemati,Used

Multilayer Potentials And Boundary Problems: For Higherorder Elliptic Systems In Lipschitz Domains (Lecture Notes In Mathemati,Used

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Many 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 higherorder (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 Caldern, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higherorder 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 higherorder elliptic operators in nonsmooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in nonsmooth domains including layer potentials, jump relations, nontangential maximal function estimates, multitraces and extensions, boundary value problems with data in WhitneyLebesque spaces, WhitneyBesov spaces, WhitneySobolev based Lebesgue spaces, WhitneyTriebelLizorkin spaces,WhitneySobolevbased Hardy spaces, WhitneyBMO and WhitneyVMO spaces.

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