调和微分形式的一个反边界值问题
偏微分方程分析
2008-07-31 v3
摘要
我们证明，具有边界的黎曼流形（维数大于 2）上 k-形式 Laplace 方程的 Dirichlet 到 Neumann 映射的全符号决定了度量在边界处的全 Taylor 级数。这推广了 Lee 与 Uhlmann 在 情形的结果。证明中通过使用以边界法向坐标为参数的拟微分算子演算并递归计算边界算子之差的主符号，避免了全符号的计算。
引用
@article{arxiv.math/9911212,
title = {An inverse boundary value problem for harmonic differential forms},
author = {M. S. Joshi and W. R. B. Lionheart},
journal= {arXiv preprint arXiv:math/9911212},
year = {2008}
}
备注
In this revision the assumption that the normal is known has been removed. The paper also benefits from comments at the ICMS Conference: Tomographic Inverse Problems,Edinburgh 3-5 August 2000. The second revision has a version of the theorem with more natural Neumann data