PARABOLIC SYSTEMS WITH MEASURABLE COEFFICIENTS IN WEIGHTED SOBOLEV SPACES - Kim, Doyoon; Kim, Kyeong Hun; Lee, Kijung (Communications on Pure and Applied Analysis, 2022)
We present a weighted Lp-theory of parabolic systems on a half space Rd+. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.
Keywords: measurable coefficients; parabolic systems; sharp/maximal functions; weighted Sobolev spaces