From the 1 of 5 linked papers with an AI index.
5 papers
Riesz energy deformation through insulated strips
Carrie Clark, Richard S. Laugesen
The paper shows that Riesz energies with exponents differing by one appear as limiting cases of a family of infinite‑strip energies with Neumann boundary conditions, and uses this…
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…
Two disks maximize the third Robin eigenvalue: positive parameters
Hanna N. Kim, Richard S. Laugesen
The third eigenvalue of the Robin Laplacian on a simply-connected planar domain of given area is bounded above by the corresponding eigenvalue of a disjoint union of two equal disk…
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…
Maximizing Riesz capacity ratios: conjectures and theorems
Carrie Clark, Richard S. Laugesen
A shape optimization program is developed for the ratio of Riesz capacities , where ranges over compact sets in . In different re…