SEMINAIRE MERCREDI 28 JUIN 2006
11 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Groupe de travail des CPT-LATP: (GOMS)
Guides d'Ondes, Milieux Stratifiés et Diffusion par des Surfaces
www.latp.univ-mrs.fr/seminaire/goms/

14h-15h: Matania Ben-Artzi
Institute of Mathematics, Hebrew University, Jerusalem

Title: Resolvent estimates at thresholds

Abstract: We consider the class of elliptic self-adjoint operators of
"divergence-form", namely, L=-D_i a_{i,j} D_j , where (a_{i,j}(x))_{1
\leq i,j \leq n} is a positive definite matrix for every x \in R^n. In
addition we assume that L is uniformly elliptic. Such operators appear
frequently in mathematical physics (e.g., elasticity theory, acoustic
generators with variable speed-of-sound etc.). Furthermore, they have
a geometric meaning (expressing the Laplace-Beltrami operator on a
manifold). They have some very interesting spectral properties (with
physical analogs such as "waveguides"). We shall discuss some results
related to the "Limiting Absorption Principle" and resolvent estimates
for this class of operators. Special attention will be given to
estimates near thresholds, in particular the bottom of the (essential)
spectrum.

15h: Pause café

15h15: Discussions