We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b∈Ln/2+δ where δ>0. As an application we provide a one-sided Liouville's theorem provided that b∈Ln/2+δ(ℝn).
All Science Journal Classification (ASJC) codes
- Applied Mathematics
- Drift-diffusion equations
- Harnack inequality
- Liouville theorem