Scalar elliptic equations with a singular drift
Misha Chernobai, Timofey Shilkin · Complex Variables and Elliptic Equations · 2020
We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation −Δu+b(α)⋅∇u=f in a bounded domain Ω⊂R2 containing the origin, where f∈Wq−1(Ω) with q>2 and b(α):=b−αx|x|2, b is a divergence-free vector field and α∈R is a parameter.