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This paper is a comprehensive study of $L_p$ estimates for time fractional wave equations of order $alpha in (1,2)$ in the whole space, a half space, or a cylindrical domain. We obtain weighted mixed-norm estimates and solvability of the equations in both non-divergence form and divergence form when the leading coefficients have small mean oscillation in small cylinders.
We consider Stokes systems in non-divergence form with measurable coefficients and Lions-type boundary conditions. We show that for the Lions conditions, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm $L_{s,q}$-estimates
We prove the mixed-norm Sobolev estimates for solutions to both divergence and non-divergence form time-dependent Stokes systems with unbounded measurable coefficients having small mean oscillations with respect to the spatial variable in small cylin
We study a class of elliptic and parabolic equations in non-divergence form with singular coefficients in an upper half space with the homogeneous Dirichlet boundary condition. Intrinsic weighted Sobolev spaces are found in which the existence and un
In this paper, we study both elliptic and parabolic equations in non-divergence form with singular degenerate coefficients. Weighted and mixed-norm $L_p$-estimates and solvability are established under some suitable partially weighted BMO regularity
We give a unified approach to weighted mixed-norm estimates and solvability for both the usual and time fractional parabolic equations in nondivergence form when coefficients are merely measurable in the time variable. In the spatial variables, the l