Solution to nonlinear parabolic equations related to P-Laplacian

Consider the following Cauchy problem: u(t) = div(vertical bar del u(m)vertical bar(p-2)del u(m)), (x, t) is an element of S-T = R-N x (0, T), u(x, 0) = mu, x is an element of R-N, where 1 < p < 2, 1 < m < 1/p-1 and mu is a sigma-finite measure in R-N . By the Moser's iteration method, the existence of the weak solution is obtained, provided that (m+1)N/mN+1 < p. In contrast, if , (m+1)N/mN+1 >= p, there is no solution to the Cauchy problem with an initial value delta(x), where delta(x) is the classical Dirac function.