Recent Progress in the Lp Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients  

作　　者：Hongjie Dong 

机构地区：[1]Division of Applied Mathematics,Brown University,182 George Street,Providence,RI 02912,USA

出　　处：《Analysis in Theory and Applications》2020年第2期161-199,共39页分析理论与应用（英文刊）

摘　　要：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 VMOx 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 Lp estimates with Muckenhoupt(Ap)weights,non-local elliptic and parabolic equations,as well as fully nonlinear elliptic and parabolic equations.

关 键 词：Elliptic and parabolic equations and systems nonlocal equations fully nonlinear equations VMO and partially VMO coefficients weighted estimates Muckenhoupt weights 

分 类 号：O175.2[理学—数学]