Asymptotic of the Heat Kernel in Unbounded Domains
Pierre Collet · Birkhäuser Basel eBooks · 2003
We prove ratio limit theorems (Davies conjecture) for the heat kernel in unbounded domains with Dirichlet boundary conditions under some accessibility assumptions on the boundary. In the case of Benedicks domains when the cone of positive harmonic functions which tend to zero at the boundary is nontrivial we derive the explicit asymptotic for the case with compact holes. We refer to the original papers by S. Martínez, J. San Martín and the author for the general case.