论文标题
谐波功能和应用梯度的张量产物的密度特性
A density property for tensor products of gradients of harmonic functions and applications
论文作者
论文摘要
我们表明，对于任何有限的域$ω$，在$ c（\overlineΩ）$中，均值$ k $的张量梯度梯度至少三个，在$ c（\overlineΩ）中均以3或更高的限制域$ω$。大部分论点包括表明，所有此类产品的平滑紧凑型$ k $ tensor均为$ l^2 $ - 接地均必须为零。这是通过在正交关系中使用基于高斯准模式的谐波函数的构造来完成的。然后，我们通过使用它来证明该结果的有用性来证明耦合的准线性椭圆系统的逆边界值问题的唯一性。本文以对两个谐波函数梯度的产品的相应属性的讨论以及该属性与线性性各向异性Calderón问题的联系结束。
We show that tensor products of $k$ gradients of harmonic functions, with $k$ at least three, are dense in $C(\overlineΩ)$, for any bounded domain $Ω$ in dimension 3 or higher. The bulk of the argument consists in showing that any smooth compactly supported $k$-tensor that is $L^2$-orthogonal to all such products must be zero. This is done by using a Gaussian quasi-mode based construction of harmonic functions in the orthogonality relation. We then demonstrate the usefulness of this result by using it to prove uniqueness in the inverse boundary value problem for a coupled quasilinear elliptic system. The paper ends with a discussion of the corresponding property for products of two gradients of harmonic functions, and the connection of this property with the linearized anisotropic Calderón problem.
