MAXIMAL SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH LOCALLY INTEGRABLE FORCING TERM

Moshe Marcus (1) , Laurent Veron (2)

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

We study the existence of a maximal solution of $-\Gd u+g(u)=f(x)$ in a domain $\Gw\subset \BBR^N$ with compact boundary, assuming that $f\in (L^1_{loc}(\Gw))_+$ and that $g$ is nondecreasing, $g(0)\geq 0$ and $g$ satisfies the Keller-Osserman condition. We show that if the boundary satisfies the classical $C_{1,2}$ Wiener criterion then the maximal solution is a large solution, i.e., it blows up everywhere on the boundary. In addition we discuss the question of uniqueness of large solutions.

Mots clés: Elliptc equations

Domaines: Equations aux dérivées partielles [math.AP]

Moshe Marcus, Laurent Veron. MAXIMAL SOLUTIONS OF SEMILINEAR ELLIPTIC EQUATIONS WITH LOCALLY INTEGRABLE FORCING TERM. Israel Journal of Mathematics, 2006, 152, pp.333-348. ⟨hal-00280100⟩