Neumann Bessel Heat Kernel Monotonicity
✍ Scribed by R. Bañuelos; T. Kulczycki; B. Siudeja
- Publisher
- Springer Netherlands
- Year
- 2008
- Tongue
- English
- Weight
- 414 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0926-2601
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We consider the challenging problem of Chavel's conjecture on the domain monotonicity of the fundamental solution of the Neumann problem. It says that if \(D \subset \tilde{D}\) are open convex domains and if \(p_{t}(x, y)\) and \(\tilde{p}_{t}(x, y)\) denote the corresponding parabolic heat kernels
## Abstract In this article we use classical formulas involving the __K__–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromo