A rearrangement minimization problem corresponding to<i>p</i>-Laplacian equation

In this paper a rearrangement minimization problem corresponding to solutions of the p -Laplacian equation is considered. The solution determines optimal way exerting external forces on membrane in order have minimum displacement. Geometrical and topological properties optimizer derived analytical obtained for circular annular membranes. Then, we find nearly which are shown be good approximations minimizer specific ranges parameter values optimization problem. A robust efficient numerical algorithm developed based upon techniques derive domains with different geometries ? 2 3 .