论文标题
最小表面方程的逆问题
An inverse problem for the minimal surface equation
论文作者
论文摘要
我们使用高阶线性化方法研究Riemannian歧管$（\ Mathbb {r}^n，g）$上最小表面方程的反向边界值问题，其中度量$ g $是互联的。特别是，我们表明，借助与最小表面方程相关的Dirichlet到Neumann地图，可以确定$ x_n = 0 $的泰勒级数$ c（x）$ c（x）$，达到乘法常数。我们在完整的数据案例和某些部分数据案例中都显示了这一点。
We use the method of higher order linearization to study an inverse boundary value problem for the minimal surface equation on a Riemannian manifold $(\mathbb{R}^n,g)$, where the metric $g$ is conformally Euclidean. In particular we show that with the knowledge of Dirichlet-to-Neumann map associated to the minimal surface equation, one can determine the Taylor series of the conformal factor $c(x)$ at $x_n=0$ up to a multiplicative constant. We show this both in the full data case and in some partial data cases.
