On the equation $-\mathrm{\Delta }u+e^u-1=0$ with measures as boundary data

If $\mathrm{\Omega }$ is a bounded domain in ${\mathbb{R}}^N$, we study conditions on a Radon measure $\mu$ on $\mathrm{\partial }\mathrm{\Omega }$ for solving the equation $-\Delta u+e^{u}-1=0$in$\Omega$with$u=\mu$on$\partial\Omega$. The conditions are expressed in terms of Orlicz capacities.