6 citations · 8 across the 5 of their papers we have counts for
6 papers
Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders
Pierre Bérard, Bernard Helffer, Rola Kiwan
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp…
Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
Pierre Bérard, Bernard Helffer, Rola Kiwan
The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp…
Dirichlet eigenfunctions on the cube, sharpening the Courant nodal inequality
Bernard Helffer, Rola Kiwan
This paper is devoted to the refine analysis of Courant's theorem for the Dirichlet Laplacian. Many papers (and some of them quite recent) have investigated in which cases this ine…
Where to place a spherical obstacle so as to maximize the second Dirichlet eigenvalue
Ahmad El Soufi, Rola Kiwan
We prove that among all doubly connected domains of bounded by two spheres of given radii, the second eigenvalue of the Dirichlet Laplacian achieves its maximum when…
Extremal first Dirichlet eigenvalue of doubly connected plane domains and dihedral symmetry
Ahmad El Soufi, Rola Kiwan
We deal with the following eigenvalue optimization problem: Given a bounded domain , how to place an obstacle of fixed shape within so as to maximize or mini…
Blow-up results for some second order hyperbolic inequalities with a nonlinear term with respect to the velocity
M. Jazar, R. Kiwan
We give sufficient conditions on the initial data so that a semilinear wave inequality blows-up in finite time. Our method is based on the study of an associated second order diffe…