RELATIVE NEWTONIAN POTENTIALS OF RADIAL FUNCTIONS AND ASYMPTOTICS IN NONLINEAR DIFFUSION

Abstract

The Newtonian potential is introduced in a relative sense for radial functions. In this way one may treat the potential theory for a larger class of functions in a unified manner for all dimensions d >= 1. As a result, Newton's theorem is revised in terms of relative potentials, which is a simpler argument that works for all dimensions d >= 1. This relative potential is then used to obtain the L(1)-convergence order O(t(-1)) as t -> infinity for radially symmetric solutions to the porous medium and fast diffusion equations. The technique is also applied to radial solutions of the p-Laplacian equations to obtain the same convergence order.