BMO estimates near the boundary for solutions of elliptic systems

Abstract

In this paper we show that the scale of Sobolev-Campanato spaces Lp,λ,s contain the general BMO-Triebel-Lizorkin spaces Fs∞,p as special cases, so that the conjecture by Triebel regarding estimates for solutions of scalar regular elliptic boundary value problems in Fs∞,p 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 Lp,λ,s containing BMO, Fs∞,p, and Morrey-Campanato spaces L2,λ as special cases. This result extends the work by the author in the scalar case.