A Schiffer-type problem for annuli with applications to stationary planar Euler flows

Alberto Enciso, Antonio J. Fernández, David Ruiz +1

If on a smooth bounded domain $\Omega \subset {\mathbb{R}}^2$ there is a nonconstant Neumann eigenfunction $u$ that is locally constant on the boundary, must $\Omega$ be a disk or an annulus? Th…