论文标题
椭圆形和抛物线类型的边界价值问题，具有负期的边界数据
Boundary Value Problems of Elliptic and Parabolic Type with Boundary Data of Negative Regularity
论文作者
论文摘要
我们研究混合尺度空间的椭圆形和抛物线边界值问题，在半空间上具有混合平滑度。目的是用负规律性的边界数据解决边界价值问题，并描述边界上解决方案的奇异性。为此，我们以混合平滑度的混合尺度得出了泊松算子的映射特性。在正常方向的平滑度不大的情况下，我们还得出了$ \ Mathcal {r} $ - 均质边界数据的部门性结果。
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half space. The aim is to solve boundary value problems with boundary data of negative regularity and to describe the singularities of solutions at the boundary. To this end, we derive mapping properties of Poisson operators in mixed scales with mixed smoothness. We also derive $\mathcal{R}$-sectoriality results for homogeneous boundary data in the case that the smoothness in normal direction is not too large.
