Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.
We establish the uniqueness of fundamental solutions to the p-Laplacian equation ut = div (|Du|p-2 Du), p > 2, defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equation ut...