BMO estimates near the boundary for solutions of elliptic systems
Date
2006-08-31
Authors
El Baraka, Azzeddine
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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.
Description
Keywords
Elliptic systems, BMO-Triebel-Lizorkin spaces, Campanato spaces
Citation
El Baraka, A. (2006). BMO estimates near the boundary for solutions of elliptic systems. <i>Electronic Journal of Differential Equations, 2006</i>(101), pp. 1-21.
Rights
Attribution 4.0 International