English

Elliptic equations with a singular drift from a weak Morrey space

Analysis of PDEs 2024-11-07 v6

Abstract

In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift bb satisfying divb0\operatorname{div} b\le 0 in Ω\Omega. We assume bb belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis x3x_3 with the asymptotic b(x)c/rb(x)\sim c/r, where r=x12+x22r=\sqrt{x_1^2+x_2^2}.

Keywords

Cite

@article{arxiv.2208.10909,
  title  = {Elliptic equations with a singular drift from a weak Morrey space},
  author = {Misha Chernobai and Timofey Shilkin},
  journal= {arXiv preprint arXiv:2208.10909},
  year   = {2024}
}
R2 v1 2026-06-25T01:54:04.695Z