Abstract
We study the behaviour of extremal eigenvalues of the Dirichlet biharmonic operator over rectangles with a given fixed area. We begin by proving that the principal eigenvalue is minimal for a rectangle for which the ratio between the longest and the shortest side lengths does not exceed 1.066459 1.066459 . We then consider the sequence formed by the minimal k k th eigenvalue and show that the corresponding sequence of minimising rectangles converges to the square as k k goes to infinity.
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