REVIEW 1 cited by
Overdetermined problems with sign-changing eigenfunctions in unbounded periodic domains
Not yet reviewed by Pith; the record is open.
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
abstract
We prove the existence of nontrivial unbounded domains $\O$ in the Euclidean space $\R^d$ for which the Dirichlet eigenvalue problem for the Laplacian on $\Omega$ admits sign-changing eigenfunctions with constant Neumann values on $\partial \Omega$. We also establish a similar result by studying a partially overdetermined problem on domains with two boundary components and opposite Neumann boundary values. The domains we construct are periodic in some variables and radial in the other variables, and they bifurcate from straight (generalized) cylinder or slab.
Forward citations
Cited by 1 Pith paper
-
Non-symmetric solutions to an overdetermined problem for the Helmholtz equation in the plane
For every integer m≥4 there are smooth non-disk domains in R^2 on which Δu+λu=0 admits a solution with constant nonzero Dirichlet and Neumann data, the first such counterexamples to the Willms-Gladwell conjecture.
Discussion (0). Continue with ORCID to comment.