  We prove well-posedness results for the Dirichlet problem in
$\mathbb{R}^{n}_{+}$ for homogeneous, second order, constant complex
coefficient elliptic systems with boundary data in generalized H\"older spaces
$\mathscr{C}^{\omega}(\mathbb{R}^{n-1},\mathbb{C}^M)$ and in generalized
Morrey-Campanato spaces $\mathscr{E}^{\omega,p}(\mathbb{R}^{n-1},\mathbb{C}^M)$
under certain assumptions on the growth function $\omega$. We also identify a
class of growth functions $\omega$ for which
$\mathscr{C}^{\omega}(\mathbb{R}^{n-1},\mathbb{C}^M)=\mathscr{E}^{\omega,p}(\mathbb{R}^{n-1},\mathbb{C}^M)$
and for which the aforementioned well-posedness results are equivalent, in the
sense that they have the same unique solution, satisfying natural regularity
properties and estimates.
