Boundary Integral Operators for Plate Bending in Domains with Corners

Abstract

The paper studies boundary integral operators of the bi-Laplacian on piecewise smooth curves with corners and describes their mapping properties in the trace spaces of variational solutions of the biharmonic equation. We formulate a direct integral equation method for solving interior and exterior mixed boundary value problems on non-smooth plane domains, analyze the solvability of the corresponding systems of integral equations and prove their strong ellipticity.