\begin{align*}
W^{m ,\Phi}(\Omega)=
\Bigl\{
& u\in L^{\Phi}(\Omega);
\text{ there exists } \{g_{\alpha}\}\in L^{\Phi}(\Omega),
\alpha=(\alpha_1,\dots,\alpha_N), \text{ such that}
\\
&\int_{\Omega}
u\frac{\partial^{\alpha}\varphi}
{\partial^{\alpha_1}x_1\dots\partial^{\alpha_N}x_N}\,dx
=(-1)^{\|\alpha\|_{S}}\int_{\Omega}g_{\alpha}\varphi \,dx,
\\
&\text{for any } \varphi\in C^{\infty}_0(\Omega)
\text{ and } \|\alpha\|_{S}\leq m \Bigr\}
\end{align*}