We prove the existence of a countable family of Delaunay type domains Omega(t) subset of M-n x R, t is an element of N, where M-n is the Riemannian manifold S-n or H-n and n >= 2, bifurcating from the cylinder B-n x R (where B-n is a geodesic ball in M-n) for which the first eigenfunction of the Laplace-Beltrami operator with zero Dirichlet boundary condition also has constant Neumann data at the boundary. In other words, the overdetermined problem {Delta(g) u + lambda u = 0 in ohm(t) u = 0 on partial derivative ohm(t) g(del u,v) = const. on partial derivative ohm(t) has a bounded positive solution for some positive constant lambda, where g is the standard metric in M-n x R. The domains Omega(t) are rotationally symmetric and periodic with respect to the R-axis of the cylinder and the sequence {Omega(t)}(t) converges to the cylinder B-n x R.

- Publisher
- EDP SCIENCES S A

- Issue Date
- 2016-01

- Language
- English

- Article Type
- Article

- Keywords
MINIMAL-SURFACES; FREE-BOUNDARY; SYMMETRY; SPACE

- Citation
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, v.22, no.1, pp.1 - 28

- ISSN
- 1292-8119

- Appears in Collection
- MA-Journal Papers(저널논문)

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