Abstract
The explicit form of all possible variants of the Green formula is described for a boundary value problem when the “basic” operator is an arbitrary partial differential operator with variable matrix coefficients and the “boundary” operators are quasi-normal with vector-coefficients. If the system possesses a fundamental solution, a representation formula for the solution is derived and boundedness properties of the relevant layer potentials, mapping function spaces on the boundary (Bessel potential, Besov, Zygmund spaces) into appropriate weighted function spaces on the domain are established. We conclude by discussing some closely related topics: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae, Calderon projections, and minimal smoothness requirements for the surface and coefficients.
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