Abstract
We investigate the interior nodal sets of Steklov eigenfunctions on connected and compact surfaces with boundary. The optimal vanishing order of Steklov eigenfunctions is shown be . The singular sets consist of finitely many points on the nodal sets. We are able to prove that the Hausdorff measure is at most . Furthermore, we obtain an upper bound for the measure of interior nodal sets, . Here the positive constants depend only on the surfaces.
Citation
Jiuyi Zhu. "Interior nodal sets of Steklov eigenfunctions on surfaces." Anal. PDE 9 (4) 859 - 880, 2016. https://doi.org/10.2140/apde.2016.9.859
Information