Boundary Value Problems for Second-Order Elliptic Operators Satisfying a Carleson Condition
Boundary Value Problems for Second-Order Elliptic Operators Satisfying a Carleson Condition
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满足卡尔森条件的二阶椭圆算子的边值问题
DOI：
10.1002/cpa.21649
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发表时间：
2016
影响因子：
3
通讯作者：
Dindoš M
中科院分区：
文献类型：
--
作者：
Dindoš M
设Ω是中的Lipschitz域，并且是散度形式的二阶椭圆算子。我们建立了具有小Lipschitz常数的算子Lon Lipschitz域的Dirichlet正则性问题和Neumann问题的可解性。我们允许算子L的系数是粗糙的，服从一定的小范数Carleson条件。这些结果完善了Dindovich，Petermichl和Pipher（2007）的结果，其中Dirichlet问题在相同的假设下被考虑，以及Dindovich和Rule（2010）的结果，其中正则性和Neumann问题在二维域上被考虑。
Let Ω be a Lipschitz domain in , and be a second‐order elliptic operator in divergence form. We establish the solvability of the Dirichlet regularity problem with boundary data in and of the Neumann problem with data for the operatorLon Lipschitz domains with small Lipschitz constant. We allow the coefficients of the operatorLto be rough, obeying a certain Carleson condition with small norm. These results complete the results of Dindoš, Petermichl, and Pipher (2007), where the Dirichlet problem was considered under the same assumptions, and Dindoš and Rule (2010), where the regularity and Neumann problems were considered on two‐dimensional domains.© 2016 Wiley Periodicals, Inc.