Bekarys Bekmaganbetov will give a talk on 09/09/2025.

In this talk, I will discuss some recent results on solvability and estimates for parabolic and elliptic equations and systems on the half-space ${x_d>0}$ in weighted mixed-norm $L_p$ spaces, with either the Dirichlet or conormal boundary condition. The coefficients may degenerate or blow up near the boundary at a rate $x_d^{\alpha}$ for some parameter $\alpha$. The leading coefficients are assumed to be merely measurable in the $x_d$ variable and have vanishing mean oscillations (VMO) in the other variables. I will discuss some common tools and ideas used to prove results of such type.