PUB - Publikationen an der Universität Bielefeld

In terms of the upper bounds of a second-order elliptic operator acting on specific Lyapunov-type functions with compact level sets, sufficient conditions are presented for the corresponding Dirichlet form to satisfy the Poincare and the super-Poincare inequalities. Here, the elliptic operator is assumed to be symmetric on L-2(mu) with some probability measure mu. As applications, proofs are given for a class of (non-symmetric) diffusion operators generating Co-semigroups on L-1(mu): that their L-p(mu)-essential spectrum is empty for p > 1. This follows since it is proved that their Co-semigroups are compact.