Capacitary representations of positive solutions of semilinear parabolic equations

Details Capacitary representations of positive solutions of semilinear parabolic equations Capacitary representations of positive solutions of semilinear parabolic equations

2008-05-23

arxiv.org/abs/0805.3660v1

C. R. Acad. Sci. Paris Ser. I Paris 342 (2006) 655-660

Mathematics

Analysis of PDEs

Scientific paper

We give a global bilateral estimate on the maximal solution $\bar u_F$ of $ \prt_tu-\Delta u+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 $\sigma$-moderate in Dynkin's sense.

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