  We present some new regularity criteria for ``suitable weak solutions'' of
the Navier-Stokes equations near the boundary in dimension three. We prove that
suitable weak solutions are H\"older continuous up to the boundary provided
that the scaled mixed norm $L^{p,q}_{x,t}$ with $3/p+2/q\leq 2, 2<q\le \infty$,
$(p,q) \not = (3/2,\infty)$, is small near the boundary. Our methods yield new
results in the interior case as well. Partial regularity of weak solutions is
also analyzed under some conditions of the Prodi-Serrin type.
