We consider the Poisson problem on varying, possibly unbounded domains with bounded source term. Extending the solutions by zero outside the domain we get a uniformly bounded sequence of functions on RN. We discuss conditions under which the sequence of solutions converge (locally) uniformly on RN. The concept of regular convergence is introduced implying local uniform convergence of solutions. Regular convergence is rather general. For instance we can cut into a domain, or the difference in measure between the sequence of domains and the limit domain does not need to go to zero.