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

Abstract

If $\Omega$ is a bounded domain in ${\mathbb{R}}^N$, we study conditions on a Radon measure $\mu$ on $\partial \Omega$ 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.

Version détaillée de la note préliminaire hal-00573805