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We consider the Steklov-Dirichlet eigenvalue problem on eccentric annuli inEuclidean space of general dimensions. In recent work by the same authors ofthis paper [21], a limiting behavior of the first eigenvalue, as the distancebetween the two boundary circles of an annulus approaches zero, was obtained intwo dimensions. We extend this limiting behavior to general dimensions byemploying bispherical coordinates and expressing the first eigenfunction as aFourier-Gegenbauer series.

On the first Steklov-Dirichlet eigenvalue on eccentric annuli in general dimensions