On the lowest eigenvalue of the Laplacian for the intersection of two domains.
On the Principal Eigenvalue of a Second Order Linear Elliptic Problem with an Indefinite Weight Function.
On the principal eigenvalue of elliptic operators in and applications
Two generalizations of the notion of principal eigenvalue for elliptic operators in are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.
On the Principal Eigenvalues of Indefinite Elliptic Problems.
On the spectrum of a nonlinear planar problem
On the Spectrum of Non-Compact Manifolds with Finite Volume.
On torsional rigidity and principal frequencies: an invitation to the Kohler−Jobin rearrangement technique
We generalize to the p-Laplacian Δp a spectral inequality proved by M.-T. Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of Δp of a set in terms of its p-torsional rigidity. The result is valid in every space dimension, for every 1 < p < ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants. The method of proof...
Opérateurs de Schrödinger avec champ magnétique
Optimal potentials for Schrödinger operators
We consider the Schrödinger operator on , where is a given domain of . Our goal is to study some optimization problems where an optimal potential has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.