An inequality for Steklov eigenvalues for planar domains
β Scribed by Julian Edward
- Book ID
- 105014955
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 191 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0044-2275
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let (M n , g) be a compact Riemannian manifold with boundary. In this paper we give upper and lower estimates for the first nonzero Steklov eigenvalue where & 1 is a positive real number. The estimate from below is for a star-shaped domain on a manifold whose Ricci curvature is bounded from below.
Each eigenvalue of the Laplacian, subject to Dirichlet boundary conditions, is shown to attain its extremes over those open planar starlike sets that simultaneously (i) contain a given disk, (ii) occupy a given area, and (iii) do not exceed a prescribed perimeter. Over that subclass of starlike sets