scholarly journals Lower bounds for interior nodal sets of Steklov eigenfunctions

2016 ◽  
Vol 144 (11) ◽  
pp. 4715-4722 ◽  
Author(s):  
Christopher D. Sogge ◽  
Xing Wang ◽  
Jiuyi Zhu
Keyword(s):  
Lower Bounds ◽  
Nodal Sets ◽  
Steklov Eigenfunctions

scholarly journals Lower Bounds for Nodal Sets of Eigenfunctions

2011 ◽  
Vol 306 (3) ◽  
pp. 777-784 ◽  
Author(s):  
Tobias H. Colding ◽  
William P. Minicozzi
Keyword(s):  
Lower Bounds ◽  
Nodal Sets

scholarly journals Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces

2019 ◽  
Vol 2019 (754) ◽  
pp. 17-47 ◽  
Author(s):  
Iosif Polterovich ◽  
David A. Sher ◽  
John A. Toth
Keyword(s):  
Lower Bounds ◽  
Harmonic Functions ◽  
Frequency Function ◽  
Upper And Lower Bounds ◽  
Riemannian Surfaces ◽  
Real Analytic ◽  
Steklov Eigenfunctions

Abstract We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface as well as the construction of exponentially accurate approximations for the Steklov eigenfunctions near the boundary.

scholarly journals Nodal Sets of Steklov Eigenfunctions near the Boundary: Inner Radius Estimates

2021 ◽  
Author(s):  
Stefano Decio
Keyword(s):  
Lipschitz Domain ◽  
Nodal Domain ◽  
Nodal Sets ◽  
Bounded Lipschitz Domain ◽  
Inner Radius ◽  
Steklov Eigenfunctions

Abstract We show that Steklov eigenfunctions in a bounded Lipschitz domain have wavelength dense nodal sets near the boundary, in contrast to what can happen deep inside the domain. Conversely, in a 2D Lipschitz domain $\Omega $, we prove that any nodal domain of a Steklov eigenfunction contains a half-ball centered at $\partial \Omega $ of radius $c_{\Omega }/{\lambda }$.

scholarly journals Lower bounds on the Hausdorff measure of nodal sets II

2012 ◽  
Vol 19 (6) ◽  
pp. 1361-1364 ◽  
Author(s):  
Christopher D. Sogge ◽  
Steve Zelditch
Keyword(s):  
Lower Bounds ◽  
Hausdorff Measure ◽  
Nodal Sets
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