论文标题
椭圆形问题与广义Sobolev空间中的粗糙边界数据
Elliptic problems with rough boundary data in generalized Sobolev spaces
论文作者
论文摘要
我们研究了有限域中的常规椭圆边界值问题，并以内部产物Sobolev空间（任意真实的实际订单）和相应的插值Hilbert Space形成的扩展量表显示了相关运算符的Fredholm性质。特别是，我们可以以任意低规律性处理边界数据。此外，我们还显示了扩展量表，嵌入结果以及全球和本地的插值特性，用于研究所研究问题的解决方案的先验估计。结果应用于右侧均匀的椭圆问题，以及在Nikoskii空间中具有粗糙边界数据的椭圆问题，这使我们能够处理边界上的某些白噪声情况。
We investigate regular elliptic boundary-value problems in bounded domains and show the Fredholm property for the related operators in an extended scale formed by inner product Sobolev spaces (of arbitrary real orders) and corresponding interpolation Hilbert spaces. In particular, we can deal with boundary data with arbitrary low regularity. In addition, we show interpolation properties for the extended scale, embedding results, and global and local a priori estimates for solutions to the problems under investigation. The results are applied to elliptic problems with homogeneous right-hand side and to elliptic problems with rough boundary data in Nikoskii spaces, which allows us to treat some cases of white noise on the boundary.
