Hardy inequalities and some critical elliptic and parabolic problems

We study the behaviour of the nonlinear critical p-heat equation (and the related stationary p-laplacian equation) [GRAPHICS] where -Delta(p)u = -div(\del u\(p-2)del u), f(x)greater than or equal to 0 verifying convenient regularity assumptions, Omega is a bounded domain in R-N such that 0 is an element of Omega, and 1<p<N. The analysis reveals that the behaviour depends on p. The results depend in general on the relation between it and the best constant in Hardy's inequality. (C) 1998 Academic Press.