Title: Applications of the Multilevel Analysis to Regularity Estimates for PDE


			   Constantin Bacuta
		       Department of Mathematics
		         Penn State University
                University Park, State College, PA 16802
                       Email: bacuta@math.psu.edu 
                 Web page: http://www.math.psu.edu/bacuta/


Abstract:
The multilevel representation of Sobolev norms on bounded
domains  can be viewed as the Fourier representation of Sobolev  norms on
the whole space. Some embedding relation between various interpolation
spaces on bounded domains can be efficiently analyzed using tools from
multilevel (multigrid) theory. As a consequence,  regularity estimates for
elliptic boundary value problems on polygonal domains in terms of Sobolev
and Besov norms are proved. New sharp finite element error estimates
are deduced.