标题： 适定性受扰与高阶椭圆系统层位势的粗糙系数 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： 本文研究了发散形式的高阶椭圆微分算子的边值问题。我们考虑了两个密切相关的问题：非齐次问题和具有分数光滑性空间边界数据的问题。我们建立了关于非齐次问题在分数光滑性空间中边界数据的适定性的 $L^\infty$ 扰动结果。结合早期已知的结果，这使我们能够建立新的适定性结果，针对系数接近实数且与t无关的二阶算子以及接近双调和算子的四阶算子。 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 establish $L^\infty$ perturbative results concerning well posedness of inhomogeneous problems with boundary data in fractional smoothness spaces. Combined with earlier known results, this allows us to establish new well posedness results for second order operators whose coefficients are close to being real and t-independent and for fourth-order operators close to the biharmonic operator.