Robin spectrum: two disks maximize the third eigenvalue

Published 30 Jul 2019 in math.SP and math.AP | (1907.13173v1)

Abstract: The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the third eigenvalue of a disjoint union of two disks, provided the Robin parameter lies in a certain range and is scaled in each case by the length of the boundary. Equality is achieved when the domain degenerates suitably to the two disks.

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