Capacitary representations of positive solutions of semilinear parabolic equations

Moshe Marcus; Laurent Veron

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arXiv · 0805.3660

Capacitary representations of positive solutions of semilinear parabolic equations

Moshe Marcus·Laurent Veron

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Abstract

We give a global bilateral estimate on the maximal solution $\bar u_F$ of $ \prt_tu-Δu+u^q=0$ in $\BBR^N\times (0,\infty)$, $q>1$, $N\geq 1$, which vanishes at $t=0 $ on the complement of a closed subset $F\subset \BBR^N$. This estimate is expressed by a Wiener test involving the Bessel capacity $C_{2/q,q'}$. We deduce from this estimate that $\bar {u}_F$ is $σ$-moderate in Dynkin's sense.

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Moshe Marcus, Laurent Veron. 2008-05-23. Capacitary representations of positive solutions of semilinear parabolic equations. https://arxiv.org/abs/0805.3660

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