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A partially covered cavity, or trench, located along the edge of two intersecting metallic walls perpendicular to each other is considered. The cross-section of the cavity is a quarter ellipse and is slotted along the interfocal distance. The cavity is filled with a material isorefractive to that occupying the quarter-space between the walls. This two-dimensional boundary-value problem is solved exactly, when the primary field is either a plane wave of arbitrary polarization and direction of incidence or an electric or magnetic line source. Numerical results are given and discussed.