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math.AP2025
Payne's nodal line conjecture fails on doubly-connected planar domains
Pedro Freitas, Roméo Leylekian
We present examples of bounded planar domains with one single hole for which the nodal line of a second Dirichlet eigenfunction is closed and does not touch the boundary. This show…
math.AP2025
Extremal problems for clamped plates under tension
Pedro Freitas, Roméo Leylekian
We address extremum problems for spectral quantities associated with operators of the form with Dirichlet boundary conditions, for non-negative values of . The focus is…
math.AP2025
Fourth order Saint-Venant inequalities: maximizing compliance and mean deflection among clamped plates
Mark Ashbaugh, Dorin Bucur, Richard S. Laugesen +1
We prove a fourth order analogue of the Saint-Venant inequality: the mean deflection of a clamped plate under uniform transverse load is maximal for the ball, among plates of presc…