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

Laurent Veron

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

Analysis of PDEs 2011-03-17 v1

Authors: Laurent Veron

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.

Keywords

bounded domains boundary value problems

Cite

@article{arxiv.1103.3023,
  title  = {On the equation $-\Delta u+e^{u}-1=0$ with measures as boundary data},
  author = {Laurent Veron},
  journal= {arXiv preprint arXiv:1103.3023},
  year   = {2011}
}

Comments

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

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