论文标题
$ L_P $理论的最新进展，用于椭圆和抛物线方程的不连续系数
Recent progress in the $L_p$ theory for elliptic and parabolic equations with discontinuous coefficients
论文作者
论文摘要
在本文中，我们回顾了过去10 - 15年的一些结果，这些结果涉及不连续系数的椭圆形和抛物线方程。我们从N. V. Krylov给出的一种方法开始，以vmo $ _x $系数在整个空间中的抛物线方程式开始。然后，我们讨论一些随后的开发，包括带有系数的椭圆形和抛物线方程，仅在一个或两个空间方向上可以测量，加权$ L_P $估计，带有Muckenhoupt（$ a_p $）的重量，非网络椭圆形和抛物线方程，以及完全非线的非线性椭圆形等式。
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with VMO$_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$ estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.
