Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Let Omega be a bounded domain of class C-2 in R-N and let K be a compact subset of partial derivativeOmega. Assume that q greater than or equal to (N + 1))(N - 1) and denote by U-K the maximal solution of - Deltau + u(q) = 0 in Omega which vanishes on partial derivativeOmega\K. We obtain sharp upper and lower estimates for U-K in terms of the Bessel capacity C-2/q,C-q' and prove that U-K is sigma-moderate. In addition we describe the precise asymptotic behavior of U-K at points sigma is an element of K, which depends on the "density" of K at sigma, measured in terms of the capacity C-2/q,C-q'.