Scalar elliptic equations with a singular drift
Abstract
We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation $\Delta u + b^{(\al)}\cdot \nabla u= f$ in a bounded domain $\Om\subset \Bbb R^2$ containing the origin, where $f\in W^{1}_q(\Om) $ with $q>2$ and $b^{(\al)}:=b\al \frac{x}{x^2}$, $b$ is a divergencefree vector field and $\al\in \Bbb R$ is a parameter.
 Publication:

arXiv eprints
 Pub Date:
 November 2019
 arXiv:
 arXiv:1911.00401
 Bibcode:
 2019arXiv191100401C
 Keywords:

 Mathematics  Analysis of PDEs;
 35J25