Regularized trace of the inverse of the dirichlet laplacian
✍ Scribed by Milutin R. Dostanić
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 134 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0010-3640
No coin nor oath required. For personal study only.
✦ Synopsis
For the eigenvalues . n / 1 nD1 of the Dirichlet Laplacian on a bounded convex domain C, we find the sum of the series
the regularized trace of the inverse of Dirichlet Laplacian.
📜 SIMILAR VOLUMES
For the Tricomi equation with Dirichlet boundary conditions, we study the relationship between singularites at the boundary and singularities in the interior of a bounded planar region with smooth non-characteristic boundary. Necessary and sufficient conditions for interior smoothness are stated in
## Abstract It is shown that there exist domains Ω ⊂ ℝ^__N__^, which outside of some ball coincide with the strip ℝ^__N__ − 1^ × (0, π) and for which the Dirichlet Laplacian – Δ has eigenvalues within the subinterval (1, 4) of the essential spectrum (1, ∞).
## Abstract For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular cross‐section whose diameter