Interior nodal sets of Steklov eigenfunctions on surfaces
Interior nodal sets of Steklov eigenfunctions on surfaces
复制标题
表面上 Steklov 特征函数的内部节点集
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Jiuyi Zhu
中科院分区：
文献类型：
--
作者：
Jiuyi Zhu
研究了带边界的连通紧曲面上Steklov特征函数的内节点集$\mathcal{N}_\lambda$。Steklov特征函数的最优消失阶为$C\lambda$。奇异集$\mathcal{S}_\lambda$是节点集上的有限点。我们可以证明Hausdorff测度$H^0(\mathcal{S}_\lambda)\leq C\lambda^2$。进一步，我们得到了内部节点集测度的上界$H^1(\mathcal{N}_\lambda)\leq C\lambda^{\frac{3}{2}}$。这里的正常数$C$只与曲面有关。
We investigate the interior nodal sets $\mathcal{N}_\lambda$ of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be $C\lambda$. The singular sets $\mathcal{S}_\lambda$ are finite points on the nodal sets. We are able to prove that the Hausdorff measure $H^0(\mathcal{S}_\lambda)\leq C\lambda^2$. Furthermore, we obtain an upper bound for the measure of interior nodal sets $H^1(\mathcal{N}_\lambda)\leq C\lambda^{\frac{3}{2}}$. Here those positive constants $C$ depend only on the surfaces.