A note on the equation $-Δu+e^{u}-1=0$

Mathematics – Analysis of PDEs

Scientific paper

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

Scientific paper

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.

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