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

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