5 papers
On the fundamental eigenvalue ratio of the p-Laplacian
J. Fleckinger, E. M. Harrell, F. de Thélin
It is shown that the fundamental eigenvalue ratio λ_2 / λ_1 of the p-Laplacian is bounded by a quantity depending only on the dimension N and p.
Geometric lower bounds for the spectrum of elliptic PDEs with Dirichlet conditions in part
Evans M. Harrell
An extension of the lower-bound lemma of Boggio is given for the weak forms of certain elliptic operators, which have partially Dirichlet and partially Neumann boundary conditions,…
Commutators, eigenvalue gaps, and mean curvature in the theory of Schrödinger operators
Evans M. Harrell
Commutator relations are used to investigate the spectra of Schrödinger Hamiltonians, acting on functions of a smooth, compact -dimensional manifold immers…
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…
Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature
Pavel Exner, Evans M. Harrell, Michael Loss
This article is an expanded version of the plenary talk given by Evans Harrell at QMath98, a meeting in Prague, June 1998. We consider Laplace operators and Schrödinger operators w…