  We consider the Cauchy problem for the Perona-Malik equation in an open
subset of R^{n}, with Neumann boundary conditions.
  It is well known that in the one-dimensional case this problem does not admit
any global C^{1} solution if the initial condition is transcritical, namely
when the norm of the gradient of the initial condition is smaller than 1 in
some region, and larger than 1 in some other region
  In this paper we show that this result cannot be extended to higher
dimension. We show indeed that for n >= 2 the problem admits radial solutions
of class C^{2,1} with a transcritical initial condition.
