8 papers
Integral Formulas for Differential Forms on Weighted Manifolds and Applications
Fida El Chami, Ola Makhoul
In this paper, we derive a Reilly formula for differential forms on weighted manifolds with nonempty boundary. As an application of this formula, we prove a Poincaré-type inequalit…
The Buckling and Clamped Plate Problems on Differential Forms
Fida El Chami, Nicolas Ginoux, Georges Habib +2
We extend the buckling and clamped-plate problems to the context of differential forms on compact Riemannian manifolds with smooth boundary. We characterize their smallest eigenval…
Biharmonic Steklov operator on differential forms
Fida El Chami, Nicolas Ginoux, Georges Habib +1
We introduce the biharmonic Steklov problem on differential forms by considering suitable boundary conditions. We characterize its smallest eigenvalue and prove elementary properti…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary, part II
Fida El Chami, George Habib, Ola Makhoul +1
In [4], we gave a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a Riemann…
Eigenvalue Estimate for the basic Laplacian on manifolds with foliated boundary
Fida El Chami, Georges Habib, Ola Makhoul +1
In this paper, we give a sharp lower bound for the first eigenvalue of the basic Laplacian acting on basic -forms defined on a compact manifold whose boundary is endowed with a…
A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues
Said Ilias, Makhoul Ola
In this paper, we derive "universal" inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed Submanifolds and of eigenvalues of the Kohn Laplaci…
Universal inequalities for the eigenvalues of a power of the Laplace operator
Said Ilias, Ola Makhoul
In this paper, we obtain a new abstract formula relating eigenvalues of a self-adjoint operator to two families of symmetric and skew-symmetric operators and their commutators. Thi…
"Universal" inequalities for the eigenvalues of the biharmonic operator
Said Ilias, Ola Makhoul
In this paper, we establish universal inequalities for eigenvalues of the clamped plate problem on compact submanifolds of Euclidean spaces, of spheres and of real, complex and qua…