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




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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





Author: Laurent Veron -

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



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