论文标题
Riemann表面上的$ l^p $框架中的calderón问题
The Calderón problem in the $L^p$ framework on Riemann surfaces
论文作者
论文摘要
本文的目的是将二维Calderón问题的唯一性结果扩展到一般几何环境上的无界电势。我们证明，Schrödinger方程的Cauchy数据集唯一地确定了$ l^{p} $中的潜力，对于$ p> 4/3 $。在此过程中，我们首先恢复了潜力的奇异性，从那时起，可以采用基于$ l^2 $的固定相的方法。这两个步骤均通过复杂的几何视光解决方案和Carleman估算的结构完成。
The purpose of this article is to extend the uniqueness results for the two dimensional Calderón problem to unbounded potentials on general geometric settings. We prove that the Cauchy data sets for Schrödinger equations uniquely determines potentials in $L^{p}$ for $p> 4/3$. In doing so, we first recover singularities of the potential, from which point a $L^2$-based method of stationary phase can be applied. Both steps are done via constructions of complex geometric optic solutions and Carleman estimates.
