Elliptic equations with VMO a, b∈𝐿_{𝑑}, and c∈𝐿_{𝑑/2}

Krylov, N.

doi:10.1090/tran/8282

Elliptic equations with VMO a, b$\,\in L_{d}$, and c$\,\in L_{d/2}$
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by N. V. Krylov PDF

Trans. Amer. Math. Soc. 374 (2021), 2805-2822 Request permission

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 $c\in L_{q}$, $c\geq 0$, $d>q\geq d/2$. We prove the solvability of $Lu=f\in L_{p}$ in bounded $C^{1,1}$-domains, $1<p\leq q$, and of $\lambda u-Lu=f$ in the whole space for any $\lambda >0$. Weak uniqueness of the martingale problem associated with such operators is also obtained.

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