  We study existence of densities for solutions to stochastic differential
equations with H\"older continuous coefficients and driven by a $d$-dimensional
L\'evy process $Z=(Z_{t})_{t\geq 0}$, where, for $t>0$, the density function
$f_{t}$ of $Z_{t}$ exists and satisfies, for some
$(\alpha_{i})_{i=1,\dots,d}\subset(0,2)$ and $C>0$, \begin{align*}
  \limsup\limits _{t \to 0}t^{1/\alpha_{i}}\int\limits
_{\mathbb{R}^{d}}|f_{t}(z+e_{i}h)-f_{t}(z)|dz\leq C|h|,\ \ h\in \mathbb{R},\ \
i=1,\dots,d. \end{align*} Here $e_{1},\dots,e_{d}$ denote the canonical basis
vectors in $\mathbb{R}^{d}$. The latter condition covers anisotropic
$(\alpha_{1},\dots,\alpha_{d})$-stable laws but also particular cases of
subordinate Brownian motion. To prove our result we use some ideas taken from
\citep{DF13}.
