Boundary integral operators on curved polygons

Abstract

The operators of the single layer potential, double layer potential, and the Hilbert transform, acting on plane curves with corners, are members of the class of integral operators which we define in this paper. We use expansions in homogeneous kernels of increasing degree to define lower order symbols via local Mellin transforms. In this way we can study the mapping properties in (augmented) Sobolev spaces including Garding inequalities and higher regularity, thus generalizing the results of [3]and [4]from polygons to curved polygons. © 1978 Fondazione Annali di Matematica Pura ed Applicata.