33 citations · 146 across the 35 of their papers we have counts for
43 papers
Toward Pólya and Szegő's conjecture for logarithmic vs Newtonian capacity
Carrie Clark, Richard S. Laugesen
Pólya and Szegő conjectured in 1945 that the disk achieves the largest electrostatic capacity among all planar sets with given logarithmic capacity. This question generalizes natur…
Riesz energy deformation through insulated strips
Carrie Clark, Richard S. Laugesen
For compact sets in Euclidean space, Riesz energies whose exponents differ by are shown to arise as the endpoint cases of a one-parameter family of infinite-strip energies as t…
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 d…
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…