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We prove that among all doubly connected domains of ℝ  n   of the form  B  1 \ B ̅ 2 , where  B  1  and  B  2  are open balls of fixed radii such that  B ̅ 2 ⊂ B  1 , the first nonzero Steklov eigenvalue achieves its maximal value uniquely when the balls are concentric. Furthermore, we show that the ideas of our proof also apply to a mixed boundary conditions eigenvalue problem found in literature.

Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue