Trace and boundary singularities of positive solutions of a class of quasilinear equations (Q6102526)

The authors study the following class of quasilinear elliptic equations \[ -\Delta \,u +m|\nabla u|^q-|u|^{p-1}u=0\tag{1} \] in a domain \(\Omega\) of \(\mathbb{R}^N\) or in \(\mathbb{R}_+^N\) with \(p>1\) and \(1<q<2\). Under some conditions involving Bessel capacities on the boundary, the authors prove the existence of a solution to problem (1) with a nonnegative measure as boundary data. Also removability of boundary singular sets and solutions with an isolated singularity on \(\partial\Omega\) are studied.