34 citations · 117 across the 29 of their papers we have counts for
4 papers · 1 filter
On sums of eigenvalues of elliptic operators on manifolds
Ahmad El Soufi, Evans Harrell, Said Ilias +1
We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operato…
On the placement of an obstacle so as to optimize the Dirichlet heat trace
Ahmad El Soufi, Evans Harrell
We prove that among all doubly connected domains of bounded by two spheres of given radii, , the trace of the heat kernel with Dirichlet boundary conditions, achieves…
Universal inequalities for the eigenvalues of Schrodinger operators on submanifolds
Ahmad El Soufi, Evans Harrell, Said Ilias
We establish inequalities for the eigenvalues of Schrödinger operators on compact submanifolds (possibly with nonempty boundary) of Euclidean spaces, of spheres, and of real, compl…
A direct proof of a theorem of Blaschke and Lebesgue
Evans M. Harrell
The Blaschke-Lebesgue Theorem states that among all planar convex domains of given constant width B the Reuleaux triangle has minimal area. It is the purpose of the present note to…