4 papers · 1 filter
Sharp Quantitative Stability of the Dirichlet spectrum near the ball
Dorin Bucur, Jimmy Lamboley, Mickaël Nahon +1
Let be an open set with the same volume as the unit ball and let be the -th eigenvalue of the Laplace operator of with Dirichlet boun…
On Poincaré constants related to isoperimetric problems in convex bodies
Dorin Bucur, Ilaria FragalÃ
For any convex set , we provide a lower bound for the inverse of the Poincaré constant in : it refines an inequality in terms of the diam…
Spherical caps do not always maximize Neumann eigenvalues on the sphere
Dorin Bucur, Richard S. Laugesen, Eloi Martinet +1
We prove the existence of an open set for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic…
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…