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

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

2011-03-15

arxiv.org/abs/1103.3023v1

Mathematics

Analysis of PDEs

Version d\'etaill\'ee de la note pr\'eliminaire hal-00573805

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 Orlicz capacities.

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