We obtain the existence of a smooth 1-parameter family of non-compact domains Ωs⊂Mn×R, n≥2, bifurcating from the straight cylinder B1×R such that the problem (Formula presented.) has a bounded solution, where Mn is the Riemannian manifold Sn or Hn, and B1 is a unit geodesic ball in Mn. The domains Ωs are rotationally symmetric and periodic with respect to the R-axis of the cylinder. Moreover, we also show that the bifurcation is critical.
Bifurcation domains for the Serrin’s overdetermined problem in Sn×R and Hn×R
Morabito F.;
2026-01-01
Abstract
We obtain the existence of a smooth 1-parameter family of non-compact domains Ωs⊂Mn×R, n≥2, bifurcating from the straight cylinder B1×R such that the problem (Formula presented.) has a bounded solution, where Mn is the Riemannian manifold Sn or Hn, and B1 is a unit geodesic ball in Mn. The domains Ωs are rotationally symmetric and periodic with respect to the R-axis of the cylinder. Moreover, we also show that the bifurcation is critical.File in questo prodotto:
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