ﻻ يوجد ملخص باللغة العربية
We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space $mathbb{R}^d$, $d ge 3$, under the assumption that weak solutions of the system are locally Holder continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on $Omega$, where $Omega$ is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.
We study the stationary Stokes system with variable coefficients in the whole space, a half space, and on bounded Lipschitz domains. In the whole and half spaces, we obtain a priori $dot W^1_q$-estimates for any $qin [2,infty)$ when the coefficients
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 prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions, i.e., locally they are merely measurable in one direction and have s
Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian upper bound