论文标题
椭圆运算符的定量强大独特延续 - 应用于逆光谱问题
Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem
论文作者
论文摘要
基于[23]中建立的三球不平等和加倍不平等，我们量化了Koch和Tataru [21]为具有无界较低系数的椭圆算子建立的强大独特延续。我们还为本征函数得出了一个均匀的定量唯一延续，我们用来证明两个dirichlet-laplace-beltrami操作员每当它们相应的指标在边界附近重合的相应指标及其边界光谱数据重合在正量值的子集上时，它们的相应指标是相当的。
Based on the three-ball inequality and the doubling inequality established in [23], we quantify the strong unique continuation established by Koch and Tataru [21] for elliptic operators with unbounded lower-order coefficients. We also derive a uniform quantitative strong unique continuation for eigenfunctions that we use to prove that two Dirichlet-Laplace-Beltrami operators are gauge equivalent whenever their corresponding metrics coincide in the vicinity of the boundary and their boundary spectral data coincide on a subset of positive measure.
