Removable Singularities and Existence for a Quasilinear Equation with Absorption or Source Term and Measure Data

Abstract

Abstract We study the properties of the following equations with absorption or source term -Δpu = ± |u|q-1 u + μ, in a domain Ω of ℝN, where 1 < p < N, q > p-1, and μ is a Radon measure on Ω. We introduce a notion of local entropy solution, and give necessary conditions on μ for the existence of solutions, in terms of capacity. The question of removability of sets is also considered, as well as some stability results. Finally we give existence results in ℝN for the case of absorption.