A note on the equation $-\Delta u+e^u-1=0$

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 nonlinear capacities.

Preliminary report of a paper initialy written in May 2004. To appear in Mathematische Zeitschrift