标题： 不适定性的扰动及具有粗糙系数的高阶椭圆系统的层势 显示英文标题

标题： Perturbation of well-posedness and layer potentials for higher-order elliptic systems with rough coefficients

摘要： 在本文中，我们研究了高阶椭圆微分算子在散度形式下的边界值问题。 我们考虑了非齐次问题和边界数据属于分数光滑性空间的问题这两个密切相关的话题。 我们构造了这些算子的格林势和牛顿势，并利用牛顿势构造了双层和单层势；我们的构造使我们能够将二阶层势的一些标准性质推广到高阶情况。 使用这些工具，我们建立了关于分数光滑性空间中非齐次问题适定性的摄动结果和其他结果。 显示英文摘要

摘要： In this paper we study boundary value problems for higher order elliptic differential operators in divergence form. We consider the two closely related topics of inhomogeneous problems and problems with boundary data in fractional smoothness spaces. We construct the Green's potentials and the Newton potential for such operators, and use the Newton potential to construct the double and single layer potentials; our construction allows us to generalize some standard properties of second order layer potentials to the higher order case. Using these tools, we establish perturbative results and other results concerning well-posedness of inhomogeneous problems with boundary data in fractional smoothness spaces.