Scalar elliptic equations with a singular drift. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Chernobai, Misha; Shilkin, Timofey
• Is Part Of: Complex variables and elliptic equations. Volume 67:Issue 1(2022)
• Page Start: 9
• Page End: 33
• Publication Date: 2022-01-02
• Subjects: Elliptic equations -- singular drift -- weak solutions; 35J15; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1816980
• Languages: English
• ISSNs: 1747-6933

Abstract

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.