Title: On nondivergence form linear parabolic and elliptic equations with degenerate coefficients Show Chinese title

Title: 关于退化系数的非散度形式线性抛物和椭圆方程

Abstract: We establish the unique solvability in weighted mixed-norm Sobolev spaces for a class of degenerate parabolic and elliptic equations in the upper half space. The operators are in nondivergence form, with the leading coefficients given by $x_d^2a_{ij}$, where $a_{ij}$ is bounded, uniformly nondegenerate, and measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. In the remaining spatial variables, they have weighted small mean oscillations. In addition, we investigate the optimality of the function spaces associated with our results. Show Chinese abstract

Abstract: 我们建立了在加权混合范数 Sobolev 空间中一类在上半空间中的退化抛物型和椭圆型方程的唯一可解性。 这些算子以非散度形式给出，主要系数由$x_d^2a_{ij}$给出，其中$a_{ij}$在$(t,x_d)$中除了$a_{dd}$外是有界的、一致非退化的，并且在$t$或$x_d$中是可测的。 在其余的空间变量中，它们具有加权小平均振荡。 此外，我们研究了与我们的结果相关的函数空间的最优性。