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arXiv · 1911.00401

Scalar elliptic equations with a singular drift

Misha Chernobai·Timofey Shilkin
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Abstract

We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation $-\Delta u + b^{(\alpha)}\cdot \nabla u= f$ in a bounded domain $\Omega\subset {\mathbb R^2}$ containing the origin, where $f \in W^{-1}_q(\Omega) $ with $q>2$ and $b^{(\alpha)}:=b-\alpha \frac{x}{|x|^2}$, $b$ is a divergence-free vector field and $\alpha\in {\mathbb R}$ is a parameter.

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Misha Chernobai, Timofey Shilkin. 2019-11-01. Scalar elliptic equations with a singular drift. https://doi.org/10.1080/17476933.2020.1816980

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