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arXiv · 2004.01778

Elliptic equations with VMO a, b$\,\in L_{d}$, and c$\,\in L_{d/2}$

N. V. Krylov
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Abstract

We consider elliptic equations with operators $L=a^{ij}D_{ij}+b^{i}D_{i}-c$ with $a$ being almost in VMO, $b\in L_{d}$ and $c\in L_{q}$, $c\geq0$, $d>q\geq d/2$. We prove the solvability of $Lu=f\in L_{p}$ in bounded $C^{1,1}$-domains, $1 0$. Weak uniqueness of the martingale problem associated with such operators is also obtained.

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N. V. Krylov. 2020-03-22. Elliptic equations with VMO a, b$\,\in L_{d}$, and c$\,\in L_{d/2}$. https://arxiv.org/abs/2004.01778

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