Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

. Let  be a bounded domain of class C2 in RN and let K be a compact subset of ∂. Assume that q ≥ (N + 1)/(N − 1) and denote by UK the maximal solution of −1u + u q = 0 in  which vanishes on ∂ \ K . We obtain sharp upper and lower estimates for UK in terms of the Bessel capacity C2/q,q ′ and prove that UK is σ -moderate. In addition we describe the precise asymptotic behavior of UK at points σ ∈ K , which depends on the “density” of K at σ , measured in terms of the capacity C2/q,q ′ .