Boccardo, L.Gómez Castro, DavidDíaz Díaz, Jesús Ildefonso2023-06-222023-06-222022-11-21https://hdl.handle.net/20.500.14352/72748In this paper we study existence, uniqueness, and integrability of solutions to the Dirichlet problem −div(M(x)∇u)=−div(E(x)u)+f in a bounded domain of RN with N≥3. We are particularly interested in singular E with divE≥0. We start by recalling known existence results when |E|∈LN that do not rely on the sign of divE. Then, under the assumption that divE≥0 distributionally, we extend the existence theory to |E|∈L2. For the uniqueness, we prove a comparison principle in this setting. Lastly, we discuss the particular cases of E singular at one point as Ax/|x|2, or towards the boundary as divE∼dist(x,∂Ω)−2−α. In these cases the singularity of E leads to u vanishing to a certain order. In particular, this shows that the strong maximum principle fails in the presence of such singular drift terms E.engjournal articleopen access517.95Ecuaciones diferencialesFunciones (Matemáticas)1202.07 Ecuaciones en Diferencias1202 Análisis y Análisis Funcional