The L^p resolvents of second-order elliptic operators of divergence form under the Dirichlet condition

The purpose of this paper is to prove well-posedness for a problem that describes the dynamics of a set of points by means of a system of parabolic equations. It has been seen in Velazquez (Point dynamics in a singular limit of the Keller–Segel model. (1) motion of the concentration regions, SIAM J. Appl. Math., to appear) that the considered model is the limit of a singular perturbation problem for a system of the Keller–Segel type.