Weighted Sobolev spaces and regularity for polyhedral domains

✍ Scribed by Bernd Ammann; Victor Nistor

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 260 KB
• Volume: 196
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2006.10.022

✦ Synopsis

We prove a regularity result for the Poisson problem ÀDu ¼ f , uj oP ¼ g on a polyhedral domain P & R 3 using the Babus ˇka-Kondratiev spaces K m a ðPÞ. These are weighted Sobolev spaces in which the weight is given by the distance to the set of edges [4,33]. In particular, we show that there is no loss of K m a -regularity for solutions of strongly elliptic systems with smooth coefficients. We also establish a ''trace theorem'' for the restriction to the boundary of the functions in K m a ðPÞ.