Strongly Continuous Semigroups and Stochastic Representation
Genqian Liu · Journal of the London Mathematical Society · 2002
Second‐order elliptic operators realized under Dirichlet boundary conditions in bounded domains are shown to generate strongly continuous semigroups in the topology of uniform convergence. The stochastic representation and integral representation with kernel for the strongly continuous semigroups are given. Furthermore, several useful formulae for the principal eigenvalue of second‐order elliptic operators are obtained.