论文标题
关于非散落各向异性不均匀性的规律性
On the Regularity of Non-Scattering Anisotropic Inhomogeneities
论文作者
论文摘要
在本文中，我们研究了各向异性不均匀培养基在单波数和单个入射场上的必要条件。这些条件是根据不均匀性边界的规律性表示的。我们假设表征培养基的本构材料特性的系数足够光滑，并且入射波是适当非分类的。我们的分析利用了hodograph变换以及非线性椭圆形偏微分方程的规律性结果。我们的方法要求边界a-priori是$ 0 <α<1 $的类$ c^{1，α} $。
In this paper we examine necessary conditions for an anisotropic inhomogeneous medium to be non-scattering at a single wave number and for a single incident field. These conditions are expressed in terms of the regularity of the boundary of the inhomogeneity. We assume that the coefficients, characterizing the constitutive material properties of the medium, are sufficiently smooth, and the incident wave is appropriately non-degenerate. Our analysis utilizes the Hodograph transform as well as regularity results for nonlinear elliptic partial differential equations. Our approach requires that the boundary a-priori is of class $C^{1,α}$ for some $0<α<1$.
