DELAUNAY TYPE DOMAINS FOR AN OVERDETERMINED ELLIPTIC PROBLEM IN S-n x R AND H-n x R

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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
DOI
10.1051/cocv/2014064
URI
http://hdl.handle.net/10203/208021
Appears in Collection
MA-Journal Papers(저널논문)
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