We consider a system of d coupled non-linear stochastic heat equations in
spatial dimension 1 driven by d-dimensional additive space-time white noise.
We establish upper and lower bounds on hitting probabilities of the solution
{u(t,x)}t∈R+,x∈[0,1], in terms of respectively
Hausdorff measure and Newtonian capacity. We also obtain the Hausdorff
dimensions of level sets and their projections. A result of independent
interest is an anisotropic form of the Kolmogorov continuity theorem.Comment: 44 pages; submitted for publicatio