Capacitary estimates of solutions of a class of nonlinear elliptic equations

Let Omega be a smooth bounded domain in R-N and K 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 + uq = 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 UK is a-moderate. In addition we relate the strong 'blow-up' points of U-K on partial derivativeOmega to the 'thick' points of K in the fine topology associated with C-2/q,C-q' and characterize these points by a path integral condition on U-K. (C) 2003 Academie des sciences. Published by Editions scientifiques et medicales Elsevier SAS. All rights reserved.