On the Helmholtz decomposition in general unbounded domains

It is well known that the Helmholtz decomposition of L-q-spaces fails to exist for certain unbounded smooth planar domains unless q = 2, see [2], [9]. As recently shown [6], the Helmholtz projection does exist for general unbounded domains of uniform C-2-type in R-3 if we replace the space L-q, 1 < q < infinity, by L-2 boolean AND L-q for q > 2 and by L-q + L-2 for 1 < q < 2. In this paper, we generalize this new approach from the three-dimensional case to the n-dimensional case, n >= 2. By these means it is possible to define the Stokes operator in arbitrary unbounded domains of uniform C-2-type.