论文标题
某些各向异性的准椭圆方程的逆边界值问题
An inverse boundary value problem for certain anisotropic quasilinear elliptic equations
论文作者
论文摘要
在本文中，我们证明了逆边界值问题的准椭圆方程，其线性部分是laplacian，而非线性部分是溶液梯度中函数分析的差异。就结果而言，主要新颖性是允许非线性的系数为“各向异性”。与以前的作品一样，证明还原为涉及3个或更多谐波功能梯度的张量产物的积分身份。使用高斯准模型采用施工方法，我们获得了一个方便的谐波功能系列，以插入整体身份并确定我们的结果。
In this paper we prove uniqueness in the inverse boundary value problem for quasilinear elliptic equations whose linear part is the Laplacian and nonlinear part is the divergence of a function analytic in the gradient of the solution. The main novelty in terms of the result is that the coefficients of the nonlinearity are allowed to be "anisotropic". As in previous works, the proof reduces to an integral identity involving the tensor product of the gradients of 3 or more harmonic functions. Employing a construction method using Gaussian quasi-modes, we obtain a convenient family of harmonic functions to plug into the integral identity and establish our result.
