Spectral inequality and resolvent estimate for the bi-Laplace operator

A spectral estimate for the Dirac operator on Riemannian flows

We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on Sasakian and on 3-dimensional manifolds and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor. Mathematics Subject Classi...

The Resolvent for Laplace-type Operators on Asymptotically Conic Spaces

Let X be a compact manifold with boundary, and g a scattering metric on X, which may be either of short range or ‘gravitational’ long range type. Thus, g gives X the geometric structure of a complete manifold with an asymptotically conic end. Let H be an operator of the form H = ∆ + P , where ∆ is the Laplacian with respect to g and P is a self-adjoint first order scattering differential operat...

The Saint-Venant inequality for the Laplace operator with Robin boundary conditions∗

This survey paper is focused on the Saint-Venant inequality for the Laplace operator with Robin boundary conditions. In a larger context, we make the point on the recent advances concerning isoperimetric inequalities of Faber-Krahn type for elastically supported membranes and describe the main ideas of their proofs in both contexts of rearrangement and free discontinuity techniques.

Resolvent Operator Method for General Variational Inclusions

In this paper, we introduce a new class of variational inclusions involving three operator. Using the resolvent operator technique, we establish the equivalence between the general variational inclusions and the resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving the general variational inclusions. We also consider the cr...

Resolvent Estimates of the Dirac Operator