EVENT DETAILS AND ABSTRACT

Title: Resolvent estimates and global regularity for divergence-type operators
Speaker: Professor Matania Ben-Artzi
Speaker Info: Hebrew University, Israel
Brief Description:
Special Note: Special Time
Abstract:

We consider the class of elliptic self-adjoint operators of "divergence-form", namely, $L=-D_i a_{i,j} D_j +V$, 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. The main application discussed in this talk is the derivation of various global space-time estimates, to be illustrated by the Schrodinger equation as well as the wave equation. The estimates are based on an inspection of the derivative of the spectral measure at "thresholds".