论文标题
在扩展的Sobolev量表中具有非分类边界条件的椭圆问题
Elliptic problems with nonclassical boundary conditions in an extended Sobolev scale
论文作者
论文摘要
我们考虑了具有非分类边界条件的椭圆问题，这些问题包含椭圆方程域边界上的其他未知功能，还包含相对于该方程的级别的较高阶的边界运算符。我们在扩展的Sobolev量表中研究了其解决方案所指定的问题和特性的解决性。它由希尔伯特（Hilbert）广义的Sobolev空间组成，其规律性是一般径向函数$ \ MATHRM {RO} $ - 在Infinity的Avakumović的意义上变化。我们对这些空间的适当成对和定理的规律性以及对问题的广义解决方案的先验估计，对所指定问题的弗雷德霍尔姆特性建立了定理。我们获得了这些解决方案组件的精确条件，可以连续区分。
We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the order of this equation. We investigate the solvability of the indicated problems and properties of their solutions in an extended Sobolev scale. It consists of Hilbert generalized Sobolev spaces for which the order of regularity is a general radial function $\mathrm{RO}$-varying in the sense of Avakumović at infinity. We establish a theorem on the Fredholm property of the indicated problems on appropriate pairs of these spaces and theorems on the regularity and a priori estimate of the generalized solutions to the problems. We obtain exact sufficient conditions for components of these solutions to be continuously differentiable.
