Preprint
Inserted: 13 mar 2024
Last Updated: 13 mar 2024
Year: 2024
Abstract:
In two spatial dimensions, we discuss the relation between the solvability of Schiffer’s overdetermined problem and the optimisation, among sets of prescribed area, of the first eigenvalue in the buckling problem for a clamped plate and that of the first eigenvalue of the Stokes operator. For the latter, we deduce that the minimisers under area constraint that are smooth and simply connected must be discs from the fact that a pressureless velocity is a necessary condition of optimality
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