Trace and boundary singularities of positive solutions of a class of quasilinear equations

We study properties of positive functions satisfying (E) –$\mathrm{\Delta }$u+m|$\mathrm{\nabla }$u| q – u p = 0 is a domain $\mathrm{\Omega }$ or in R N + when p > 1 and 1 < q < 2. We give sufficient conditions for the existence of a solution to (E) with a nonnegative measure $\mu$ as boundary data, and these conditions are expressed in terms of Bessel capacities on the boundary. We also study removable boundary singularities and solutions with an isolated singularity on $\mathrm{\partial }$$\mathrm{\Omega }$. The different results depends on two critical exponents for p = p c := N +1 N --1 and for q = q c := N +1 N and on the position of q with respect to 2p p+1. Contents