Harmonic Analysis and Elliptic PDE

9706641 Pipher 本计画系关于调和分析技巧在线性椭圆理论中各种问题的应用。利用Littlewood-Paley理论研究了二阶发散型方程的边值问题， 特别是对于具有非光滑系数和/或其矩阵不被假设为实值或对称的方程。 在非光滑域中与线性问题有着密切的联系。因此，本项目包括研究 具有Lipschitz边界区域上的高阶椭圆算子特别是，它对待边界问题的数据在Sobolev空间或哈代空间。 在数学、物理、工程和制造业的各个领域中出现了许多问题，这些问题归结为能够在具有角和边的区域中近似求解线性偏微分方程。这种现象，即角和边的存在，导致在获得良好的近似时固有的数学困难。 特别是，重要的是能够测量误差在数据（已知量）方面有多小。 这个项目是有关制定的理论上，这些数值逼近和应用是 基于.

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.