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Linear and fully nonlinear elliptic equations with Ld -drift
Communications in Partial Differential Equations ( IF 2.1 ) Pub Date : 2020-08-17
Nicolai V. Krylov

In subdomains of R d , we consider uniformly elliptic equations H ( v ( x ) , D v ( x ) , D 2 v ( x ) , x ) = 0 with the growth of H with respect to | D v | controlled by the product of a function from Ld and | D v | . The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists d 0 ( d / 2 , d ) such that for any p ( d 0 , d ) the equation with prescribed continuous boundary data has a solution in class W p , loc 2 . Our results are new even if H is linear.



中文翻译:

具有Ld漂移的线性和完全非线性椭圆方程

在的子域中 [R d 我们考虑均匀椭圆方程 H v X d v X d 2 v X X = 0 随着H相对于 | d v | L d | d v | 假设Hx的依赖性是BMO类型。除其他外,我们证明存在 d 0 d / 2 d 这样对于任何 p d 0 d 具有规定连续边界数据的方程在类中有一个解 w ^ p 位置 2 即使H是线性的,我们的结果也是新的。

更新日期:2020-08-18
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