We describe the spectrum of the Laplacian on a manifold with asymptotically cusp ends and find asymptotics of a corresponding spectral shift function. Here the spectral shift function is the difference of the eigenvalue counting function and the scattering phase.
Weyl Asymptotic Formula for the Laplacian on Domains with Rough Boundaries
β Scribed by Yu. Netrusov; Yu. Safarov
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 315 KB
- Volume
- 253
- Category
- Article
- ISSN
- 0010-3616
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We consider the Robin boundary conditions on irregular domains where the usual Sobolev embeddings fail. We present a functional framework permitting superhomogeneous growth of the nonlinearity and prove the existence of positive, bounded, and smooth solutions of the p-Laplacian equation.
## 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 crossβsection whose diameter
## Abstract Given a domain Ξ© in β^3^ with rectifiable boundary, we consider main integral, and some other, theorems for the theory of Laplacian (sometimes called solenoidal and irrotational, or harmonic) vector fields paying a special attention to the problem of decomposing a continuous vector fiel