Capacitary strong type estimates in semilinear problems (Q1175681)

The authors consider semilinear boundary value problems of the form \(- \Delta u=u^ \gamma+f\) in \(\Omega\), \(u=0\) on \(\partial\Omega\) and \(u\) is supposed to be nonnegative. \(\Omega\) is a bounded domain of \(R^ N\), \(f\geq 0\) on \(\Omega\) and \(\gamma\in (1,\infty)\). They then study existence questions for a certain class of weak solutions.