Let \( \Gw \) be a bounded domain of class in and let be a compact subset of \( \prt\Gw \). Assume that and denote by the maximal solution of \( -\Gd u+u^q=0 \) in \( \Gw \) which vanishes on \( \prt\Gw\setminus K \). We obtain sharp upper and lower estimates for in terms of the Bessel capacity and prove that is \( \gs \)-moderate. In addition we describe the precise asymptotic behavior of at points \( \gs\in K \), which depends on the 'density' of at \( \gs \), measured in terms of the capacity .
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Moshe Marcus, Laurent Véron, Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion. J. Eur. Math. Soc. 6 (2004), no. 4, pp. 483–527DOI 10.4171/JEMS/18