论文标题
$ l^2 $限制范围的Neumann数据的改进沿Hypersurfaces
Improvements in $L^2$ Restriction bounds for Neumann Data along Hypersurfaces
论文作者
论文摘要
We seek to improve the restriction bounds of Neumann data of semiclassical Schrödinger eigenfunctions $u_h$ considered by Christianson-Hassell-Toth \cite{CHT} and Tacy \cite{Tacy2} by studying the $L^2$ restriction bounds of eigenfunctions and their $L^2$ concentration as measured by defect measures.让$γ$成为单位外部正常$ν$的平滑性超曲面。我们的主要结果说$ \ | h \partial_νu_{h} \ | _ {l^2（γ）} = o（1）$当$ \ {u_h \} $是可接受的。
We seek to improve the restriction bounds of Neumann data of semiclassical Schrödinger eigenfunctions $u_h$ considered by Christianson-Hassell-Toth \cite{CHT} and Tacy \cite{Tacy2} by studying the $L^2$ restriction bounds of eigenfunctions and their $L^2$ concentration as measured by defect measures. Let $Γ$ be a smooth hypersurface with unit exterior normal $ν$. Our main result says that $\| h \partial_νu_{h} \|_{L^2(Γ)}=o(1)$ when $\{u_h\}$ is admissible.
