For a dense family of analytic planar domains, Steklov eigenfunctions have fixed-size zero-free balls in the interior, so their nodal sets are not dense at any shrinking scale.
Nodal sets of S teklov eigenfunctions
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.AP 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Domains without dense Steklov nodal sets
For a dense family of analytic planar domains, Steklov eigenfunctions have fixed-size zero-free balls in the interior, so their nodal sets are not dense at any shrinking scale.