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arXiv · 1103.3023

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

Laurent Veron
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Abstract

If $Ω$ is a bounded domain in $\mathbb R^N$, we study conditions on a Radon measure $μ$ on $\partialΩ$ for solving the equation $-Δu+e^{u}-1=0$ in $Ω$ with $u=μ$ on $\partialΩ$. The conditions are expressed in terms of Orlicz capacities.

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Laurent Veron. 2011-03-15. On the equation $-Δu+e^{u}-1=0$ with measures as boundary data. https://arxiv.org/abs/1103.3023

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