Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
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DOI：
10.1515/crll.1988.389.1
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
G. M. Lieberman
中科院分区：
文献类型：
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作者：
G. M. Lieberman
对于适当的加权Holder类中的函数f和g。当β在3个Ω上连续且斜时，并作适当的附加假设，文[14]证明了各种结果的存在唯一性和正则性。对于不连续的β，出现了重要的技术困难，这些困难在[14]中没有出现。例如，边界条件必须在的不连续点处进行适当的解释。由于这些困难，我们只考虑β和dΩ是分段光滑的情况。我们的基本结果是下面的定理。
for functions / and g in suitable weighted Holder classes. When β is continuous and oblique on 3 Ω and appropriate additional assumptions are made, various existence, uniqueness and regularity results were proved in [14]. Important technical difficulties arise for discontinuous β which were not present in [14]. For example, the boundary condition has to be suitably interpreted at points of discontinuity of . Because of these difficulties, we consider only the case that β and d Ω are piecewise smooth. Our basic result is the following theorem.