The precise boundary trace of solutions of a class of supercritical nonlinear equations

Moshe Marcus (1) , Laurent Veron (2)

1 TECHNION - Department of Mathematics
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

We construct and study the properties of the precise boundary trace of positive solutions of $-\Delta u+u^q=0$ in a smooth bounded domain of $\mathbb R^N$, in the supercritical case $q\geq q_c=(N+1)/(N-1)$

Mots clés: Bessel capacities; capacitary measures; fine topology; Borel measures; Wiener test

Domaines: Equations aux dérivées partielles [math.AP]

Moshe Marcus, Laurent Veron. The precise boundary trace of solutions of a class of supercritical nonlinear equations. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2007, 344, pp.181-186. ⟨hal-00281805⟩