| Abstract: |
| We consider a mixed Steklov-Dirichlet eigenvalue problem on smooth bounded domains in Riemannian
manifolds. Under certain symmetry assumptions on multi-connected domains in a Euclidean space with a
spherical hole, we obtain isoperimetric inequalities for k-th Steklov- Dirichlet eigenvalues for k between 2 and
n +1 We extend Theorem 3.1 of GPPS from Euclidean domains to domains in space forms, that is, we obtain
sharp lower and upper bounds of the first Steklov-Dirichlet eigenvalue on bounded star-shaped domains in the
unit n-sphere and in the hyperbolic space.
GPPS Nunzia Gavitone, Gloria Paoli, Gianpaolo Piscitelli, and Rossano Sannipoli. An isoperimetric inequality
for the first steklov–dirichlet laplacian eigenvalue of convex sets with a spherical hole. Pacific Journal of
Mathematics, 320 (2) 241-- 259, 2023. |
|