论文标题
加权Banach空间中的高阶椭圆方程
Higher order elliptic equations in weighted Banach spaces
论文作者
论文摘要
我们考虑高阶线性，均匀的椭圆方程，并在由加权一般Banach功能空间（BFS）产生的Banach-Sobolev空间中具有非平滑系数。在BFS中，假设强壮的小木最大和Calderon-Zygmund奇异算子的界限我们在Sobolev-BFS中获得局部溶解性，并为该型的内部Schauder类型建立了先验估计。椭圆操作员。这些结果将用于获得合适的权重的加权BFS中，以获得正在考虑的操作员的弗雷德霍姆。此外，我们分析了一些加权BF的示例，这些示例验证了我们的假设，以及相应的Schauder类型估计和操作员的弗雷德霍姆斯的示例。
We consider higher order linear, uniformly elliptic equations with non-smooth coefficients in Banach-Sobolev spaces generated by weighted general Banach Function Space (BFS). Supposing boundedness of the Hardy-Littlewood Maximal and Calderon-Zygmund singular operators in BFSs we obtain local solvability in the Sobolev-BFS and establish interior Schauder type a priori estimates for the. elliptic operator. These results will be used in order to obtain Fredholmness of the operator under consideration in weighted BFSs with suitable weight. In addition, we analyze some examples of weighted BFS that verify our assumptions and in which the corresponding Schauder type estimates and Fredholmness of the operator hold true.
