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arXiv · 1707.03197

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

Nikolay Filonov·Timofey Shilkin
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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 $\operatorname{div} b=0$ turns out to be crucial.

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Nikolay Filonov, Timofey Shilkin. 2017-07-11. On some properties of weak solutions to elliptic equations with divergence-free drifts. https://doi.org/10.1090/conm%2F710

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