论文标题
边界和不规则边界数据上未知数的椭圆问题
Elliptic problems with unknowns on the boundary and irregular boundary data
论文作者
论文摘要
我们考虑了椭圆方程域边界上未知数的椭圆问题，并假设该方程的右侧是正方形的，并且边界数据是任意的（特别是不规则）的分布。我们研究了属于精制Sobolev量表的希尔伯特分布空间中通用解决方案的局部（直至边界）特性。这些空间的参数为实数和一个在无穷大时变化缓慢的函数。函数参数完善了空间的数字顺序。我们证明了有关本地规律性的定理和本地的先验估计，该解决方案对正在研究的问题进行了广义解决方案。这些定理也适用于Sobolev空间。
We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically, irregular) distributions. We investigate local (up to the boundary) properties of generalized solutions to the problem in Hilbert distribution spaces that belong to the refined Sobolev scale. These spaces are parametrized with a real number and a function that varies slowly at infinity. The function parameter refines the number order of the space. We prove theorems on local regularity and a local a priori estimate of generalized solutions to the problem under investigation. These theorems are new for Sobolev spaces as well.
