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

Abstract

We study properties of positive functions satisfying (E) --$\Delta$u+m|$\nabla$u| q -- u p = 0 is a domain $\Omega$ 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 $\partial$$\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