Parabolic Systems with measurable coefficients in weighted Sobolev spaces

Abstract

We present a weighted \begin{document}$ L_p $\end{document}-theory of parabolic systems on a half space \begin{document}$ {\mathbb{R}}^d_+ $\end{document}. The leading coefficients are assumed to be only measurable in time \begin{document}$ t $\end{document} and have small bounded mean oscillations (BMO) with respect to the spatial variables \begin{document}$ x $\end{document}, and the lower order coefficients are allowed to blow up near the boundary.