REGULARITY OF THE SOLUTIONS FOR ELLIPTIC PROBLEMS ON NONSMOOTH DOMAINS IN R-3 .2. REGULARITY IN NEIGHBORHOODS OF EDGES

This paper is the second in a series of three devoted to the analysis of the regularity of solutions of elliptic problems on nonsmooth domai ns in R-3. The present paper concentrates on the regularity of solutio ns of the Poisson equation in neighbourhoods of edges of a polyhedral domain in the framework of the weighted Sobolev spaces and countably n ormed spaces. These results can be generalised to elliptic problems ar ising from mechanics and engineering, for instance, the elasticity pro blem on polyhedral domains. Hence, the results are not only important to understand comprehensively the qualitative and quantitative aspects of the behaviours of the solution and its derivatives of all orders i n neighbourhoods of edges, but also essential to design an effective c omputation and analyse the optimal convergence of the finite elements solutions for these problems.