Regularity of the Solutions for Elliptic Problems on Nonsmooth Domains in R3.Part 1. Countably Normed Spaces on Polyhedral Domains

摘要

This is the first of a series of three devoted to the regularity of solution ofelliptic problems on nonsmooth domains in R-cubed. The present paper introduces various weighted spaces and countably weighted spaces in neighborhood of edges and vertices of polyhedral domains. These well defined spaces are the foundations for comprehensive study of the regularity theory of elliptic problem with piecewise analytic date in R-cubed.