TY - CONF
T1 - A remark on an overdetermined problem in riemannian geometry
AU - Ciraolo, Giulio
AU - Vezzoni, Luigi
PY - 2016
Y1 - 2016
N2 - Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let Ω ⊂ M be a bounded domain, with O ∈ Ω, and consider the problem Δpu = −1 in Ω with u = 0on∂Ω, where Δp is the p-Laplacian of g. We prove that if the normal derivative ∂νu of u along the boundary of Ω is a function of d satisfying suitable conditions, then Ω must be a geodesic ball. In particular, our result applies to open balls of Rn equipped with a rotationally symmetric metric of the form g = dt2 + ρ2 (t) gS, where gS is the standard metric of the sphere.
AB - Let (M, g) be a Riemannian manifold with a distinguished point O and assume that the geodesic distance d from O is an isoparametric function. Let Ω ⊂ M be a bounded domain, with O ∈ Ω, and consider the problem Δpu = −1 in Ω with u = 0on∂Ω, where Δp is the p-Laplacian of g. We prove that if the normal derivative ∂νu of u along the boundary of Ω is a function of d satisfying suitable conditions, then Ω must be a geodesic ball. In particular, our result applies to open balls of Rn equipped with a rotationally symmetric metric of the form g = dt2 + ρ2 (t) gS, where gS is the standard metric of the sphere.
KW - Comparison principle
KW - Isoparametric functions
KW - Mathematics (all)
KW - Overdetermined PDE
KW - Riemannian Geometry
KW - Rotationally symmetric spaces
KW - Comparison principle
KW - Isoparametric functions
KW - Mathematics (all)
KW - Overdetermined PDE
KW - Riemannian Geometry
KW - Rotationally symmetric spaces
UR - http://hdl.handle.net/10447/201409
UR - http://www.springer.com/series/10533
M3 - Other
SP - 87
EP - 96
ER -