The paper is devoted to study classes of plane wave diffraction problems by a region which involves a crack with impedance boundary conditions. Conditions on the wave number and impedance parameters are found to ensure the well-posedness of the problems in a scale of Bessel potential spaces. Under such conditions, representations of the solutions are also obtained upon the consideration of some associated operators which, in a sense, combine operators of Wiener-Hopf and Hankel type.
"Diffraction by a Half-plane with Different Face Impedances on an Obstacle Perpendicular to the Boundary." Commun. Math. Anal. 17 (2) 45 - 65, 2014.