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

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1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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 : Elliptic equations Orlicz capacities Reduced measures Boundary trace

Autor: Laurent Veron -

Fuente: https://hal.archives-ouvertes.fr/

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