On the location of critical point for the Poisson equation in plane ✩

The location of the unique critical point of Δu=−1 is investigated by conformal mapping method in complex variables. It is found that if the domain is given by r = 1+ p(θ), the critical point coincides with the center of mass up to the order of . However, the two do not exactly match in general as shown by simple examples. © 2005 Elsevier Inc. All rights reserved