Elliptic equations in the plane satisfying a Carleson measure condition
Elliptic equations in the plane satisfying a Carleson measure condition
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DOI：
10.4171/rmi/625
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发表时间：
2010-12
影响因子：
1.2
通讯作者：
M. Dindoš;David J. Rule
中科院分区：
文献类型：
--
作者：
M. Dindoš;David J. Rule
本文解决了（在n = 2维）系数满足极小光滑性假设（Carleson测度条件）的散度型方程div（A u）= 0的Lp Neumann和Dirichlet正则性问题对p ∈（1，∞）的某些值是否可解的公开问题. Lp Dirichlet问题的相关问题在2001年由Kenig和Pipher解决（在任何维度上）。
In this paper we settle (in dimension n = 2) the open question whether for a divergence form equation div(A∇u) = 0 with coefficients satisfying certain minimal smoothness assumption (a Carleson measure condition), the Lp Neumann and Dirichlet regularity problems are solvable for some values of p ∈ (1,∞). The related question for the Lp Dirichlet problem was settled (in any dimension) in 2001 by Kenig and Pipher [11].