## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**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".

**Date:** Wednesday, April 25, 2007

**Time:** 3:00pm

**Where:** Lunt 105

**Contact Person:** Prof. Gui-Qiang Chen

**Contact email:** gqchen@math.northwestern.edu

**Contact Phone:** 847-491-5553

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