On some properties of weak solutions to elliptic equations with divergence-free drifts

Abstract

We discuss the local properties of weak solutions to the equation $-\Delta u+b\cdot \nabla u=0$. The corresponding theory is well-known in the case $b\in L_n$, where $n$ is the dimension of the space. Our main interest is focused on the case $b\in L_2$. In this case the structure assumption $\mathrm{div}b=0$ turns out to be crucial.

References in corpus (1)

• On the loss of continuity for super-critical drift-diffusion equations

Cited by in corpus (1)

• Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures