Flexibility of Steklov eigenvalues via boundary homogenisation

Abstract Recently, D. Bucur and M. Nahon used boundary homogenisation to show the remarkable flexibility of Steklov eigenvalues planar domains. In present paper we extend their result higher dimensions arbitrary manifolds with boundary, even though in those cases does not generally exhibit any periodic structure. Our arguments use a framework variational provide different proof original results. Furthermore, an application this optimisation under perimeter constraint. It is proved that best upper bound for normalised surfaces genus zero fixed number components can always be saturated by This case actual maximisers (except simply connected surfaces) are far from being themselves. particular, it yields sharp first eigenvalue doubly