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.
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Gunther Schmidt, Boundary Integral Operators for Plate Bending in Domains with Corners. Z. Anal. Anwend. 20 (2001), no. 1, pp. 131–154DOI 10.4171/ZAA/1007