Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 101, pp. 1-21.

Title: BMO estimates near the boundary for solutions of elliptic systems

Author: Azzeddine El Baraka (Univ. Sidi Mohamed Ben Abdellah, Morocco)

Abstract: 
 In this paper we show that the scale of  Sobolev-Campanato spaces
 $\mathcal{L}^{p,\lambda,s}$ contain the general
 BMO-Triebel-Lizorkin spaces $F_{\infty,p}^{s}$ as special cases,
 so that the conjecture by Triebel regarding estimates for
 solutions of scalar regular elliptic boundary value problems in
 $F_{\infty,p}^{s}$ spaces (solved in the case $p=2$ in a previous
 work) is completely solved now.

 Also we prove that the method used for the scalar case works
 for systems, and we give a priori estimates near the boundary for
 solutions of regular elliptic systems in the general spaces
 $\mathcal{L}^{p,\lambda,s}$ containing BMO, $F_{\infty,p}^{s}$,
 and Morrey-Campanato spaces $\mathcal{L}^{2,\lambda}$
 as special cases. This result extends the work by the author
 in the scalar case.

Submitted March 2, 2006. Published August 31, 2006.
Math Subject Classifications: 35J45, 35J55.
Key Words: Elliptic systems; BMO-Triebel-Lizorkin spaces; Campanato spaces.