Capacitary estimates of solutions of semilinear parabolic equations

Moshe Marcus (1) , Laurent Veron (2)

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

We study the properties of the maximal solution u_F of the equation $u_t-\Delta u+u^q=0$ in $R^N\times R_+$ which has an initial trace concentrated on a closed subset F of R^N, in the supercritical case q\geq 1+2/N. We obtain a two sided estimate with respect to a Wiener type test involving the Bessel capacity C_{2/q,q'}. As a consequence we prove that u_F is \sigma moderate.

Mots clés: capacitary measures; Bessel capacities; Gaussian kernel; capacitary measures.

Domaines: Equations aux dérivées partielles [math.AP]

Moshe Marcus, Laurent Veron. Capacitary estimates of solutions of semilinear parabolic equations. 2006. ⟨hal-00282315v1⟩