  We consider the potentially degenerate haptotaxis system \begin{equation*}
\left\{
  \begin{aligned}
  u_t &= \nabla \cdot (\mathbb{D} \nabla u + u \nabla \cdot \mathbb{D}) - \chi
\nabla \cdot (u\mathbb{D}\nabla w) + \mu u(1-u^{r- 1}), \\
  w_t &= - uw
  \end{aligned} \right. \end{equation*} in a smooth bounded domain $\Omega
\subseteq \mathbb{R}^n$, $n \in \{2,3\}$, with a no-flux boundary condition,
positive initial data $u_0$, $w_0$ and parameters $\chi > 0$, $\mu > 0$, $r
\geq 2$ and $\mathbb{D}: \overline{\Omega} \rightarrow \mathbb{R}^{n\times n}$,
$\mathbb{D}$ positive semidefinite on $\overline{\Omega}$.
  Our main result regarding the above system is the construction of weak
solutions under fairly mild assumptions on $\mathbb{D}$ as well as the initial
data, encompassing scenarios of degenerate diffusion in the first equation. As
a step in this construction as well as a result of potential independent
interest, we further construct classical solutions for the same system under a
global positivity assumption for $\mathbb{D}$, which ensures the full
regularizing influence of its associated diffusion operator. In both
constructions, we naturally rely on the regularizing properties of a
sufficiently strong logistic source term in the first equation.
