Scalar elliptic equations with a singular drift. Issue 1 (2nd January 2022) - Chernobai, Misha; Shilkin, Timofey
ABSTRACT: We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation − Δ u + b ( α ) ⋅ ∇ u = f in a bounded domain Ω ⊂ R 2 containing the origin, where f ∈ W q − 1 ( Ω ) with q >2 and b ( α ) := b − α x | x | 2, b is a divergence-free vector field and α ∈ R is a parameter.