This paper presents a combination of the BVP-path planner and Monte Carlo localization to assist a robot in the global localization problem in sparse environments. This kind of environment poses a very difficult situation in this problem, since several of its regions do not provide relevant information to permit the robot to recover its pose. This paper proposes a strategy that distributes particles only in relevant parts of the environment using the information about the environment structure. Afterwards, it leads the robot along these regions using the numeric solution of a BVP involving Laplace equation. In the experiments, we also show that the information about robot motion can be used to improve the convergence rate to the correct robot pose. Simulation results are presented to illustrate the potential of the method.