Pith. sign in

REVIEW 2 cited by

Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1709.01891 v5 pith:VVGUMKH3 submitted 2017-09-06 math.SP math.AP

Michael Levitin , Leonid Parnovski , Iosif Polterovich , David A. Sher This is my paper · ORCID
classification math.SPmath.AP
keywords asymptoticssloshingsteklovcornerseigenvaluesmixedobtainproblem
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

In the present paper we develop an approach to obtain sharp spectral asymptotics for Steklov type problems on planar domains with corners. Our main focus is on the two-dimensional sloshing problem, which is a mixed Steklov-Neumann boundary value problem describing small vertical oscillations of an ideal fluid in a container or in a canal with a uniform cross-section. We prove a two-term asymptotic formula for sloshing eigenvalues. In particular, this confirms a conjecture posed by Fox and Kuttler in 1983. We also obtain similar eigenvalue asymptotics for other related mixed Steklov type problems, and discuss applications to the study of Steklov spectral asymptotics on polygons.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons

    math.SP 2019-08 accept novelty 8.0 of 10

    Steklov eigenvalues of curvilinear polygons are asymptotically equal to explicit quasi-eigenvalues built from side lengths and angles, with errors tending to zero.

  2. Domains without dense Steklov nodal sets

    math.AP 2019-08 accept novelty 8.0 of 10

    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.

Pith tools