We prove the existence of a non-compact smooth one-parameter family of domains Omega s. Mn xR, whereMn denotes the Riemannian manifold Sn or Hn (for n = 2), bifurcating from the straight cylinder B1 xR (where B1 is a geodesic unit ball inMn) such that there exists a positive solution u to Delta(g)u +lambda u = 0 in Omega(s) u = 0, g(del u,nu) = const on. partial derivative Omega sfor some positive constant., where g is the standard metric inM(n) xR, and nu represents the unit normal vector about. partial derivative Omega s. The domains Omega(s) are not straight cylinders but are periodic in the direction of R. This improves a previous result by the second and third author.
A Smooth 1-Parameter Family of Delaunay-Type Domains for an Overdetermined Elliptic Problem in Sn× R and Hn× R
Morabito F.;
2024-01-01
Abstract
We prove the existence of a non-compact smooth one-parameter family of domains Omega s. Mn xR, whereMn denotes the Riemannian manifold Sn or Hn (for n = 2), bifurcating from the straight cylinder B1 xR (where B1 is a geodesic unit ball inMn) such that there exists a positive solution u to Delta(g)u +lambda u = 0 in Omega(s) u = 0, g(del u,nu) = const on. partial derivative Omega sfor some positive constant., where g is the standard metric inM(n) xR, and nu represents the unit normal vector about. partial derivative Omega s. The domains Omega(s) are not straight cylinders but are periodic in the direction of R. This improves a previous result by the second and third author.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
