论文标题
带有vmo a，b $ \，\ in l_ {d} $的椭圆方程和c $ \，\ in l_ {d/2} $ in
Elliptic equations with VMO a, b$\,\in L_{d}$, and c$\,\in L_{d/2}$
论文作者
论文摘要
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 $c\in L_{q}$, $c\geq0$, $d>q\geq d/2$.我们证明了$ lu = f \ in l_ {p} $ in Bounded $ c^{1,1} $ - 域，$ 1 <p \ leq q $，以及$λu-lu = f $ in lu_ {p} $ in lu_ {p} $ in BOUNDED $ C^{1,1} $ - 对于任何$λ> 0 $。还获得了与此类操作员相关的Martingale问题的弱点。
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, $1<p\leq q$, and of $λu-Lu=f$ in the whole space for any $λ>0$. Weak uniqueness of the martingale problem associated with such operators is also obtained.
