Harmonic Analysis and Linear Elliptic Equations

Brown University, Providence RI

Investigators

Abstract

ABSTRACT This proposal has two parts. In part one, the set of problems concerns multiparameter Fourier analysis, and, in particular, a set of questions about multi-linear operators and commutators. The goal is to carry out the multi-linear theory and the Coifman-Rochberg-Weiss commutator theory to the extent possible. In part two, we consider a collection of problems concerning elliptic divergence form or non-divergence form operators with non-smooth coefficients. The proposal concerns a set of questions and problems in the general area of analysis and partial differential equations. The answers to these questions will impact scientific inquiry in any field which uses tools from "harmonic analysis" to investigate questions. Such tools have proven to be valuable in every area of the physical sciences and in many areas of the life sciences.