9706641 Pipher This project is concerned with the applications of techniques of harmonic analysis to various problems in linear elliptic theory. It uses Littlewood-Paley theory to study boundary value problems for second order divergence form equations, in particular for equations with non-smooth coefficients and/or whose matrix is not assumed to be real-valued or symmetric. There are close connections to linear problems in non-smooth domains. Thus, included in this project is the study of higher order elliptic operators in domains with Lipschitz boundary. In particular, it treats boundary problems with data in Sobolev spaces or Hardy spaces. There are many problems arising in various areas of mathematics, physics, engineering, and manufacturing which reduce to being able to approximate solutions of linear partial differential equations in regions which have corners and edges. This phenomenon, the presence of corners and edges, causes inherent mathematical difficulties in obtaining good approximations. In particular, it is important to be able to measure how small the error will be in terms of the data (the known quantities). This project is concerned with formulating the theory upon which these numerical approximations and applications are based.
