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

Laurent Veron

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

Analysis of PDEs 2011-10-27 v2

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 nonlinear capacities.

Keywords

semilinear elliptic equations bounded domains parabolic equations

Cite

@article{arxiv.1103.0975,
  title  = {A note on the equation $-\Delta u+e^{u}-1=0$},
  author = {Laurent Veron},
  journal= {arXiv preprint arXiv:1103.0975},
  year   = {2011}
}

Comments

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

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