论文标题
带有莫雷漂移和零级系数的Sobolev空间中的椭圆方程
Elliptic equations in Sobolev spaces with Morrey drift and the zeroth-order coefficients
论文作者
论文摘要
我们考虑带有操作员的椭圆方程$ l = a^{ij} d_ {ij}+b^{i} d_ {i} d_ {i} -c $，$ a $几乎在vmo中，$ b $，包含$ l_ {d} $ c \ geq0 $的Morrey类，以及$ c \ geq0 $ in Morrey class class clast $ l_}。我们证明了$ lu = f \ in l_ {p} $ in Bounded $ c^{1,1} $ domains of $ lu = f \ f \ in lu = f \的sobolev空间中的可辨率，以及$λu-lu = f $在整个空间中的任何$λ> 0 $。还讨论了与此类运营商相关的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 a Morrey class containing $ L_{d}$, and $c\geq0$ in a Morrey class containing $L_{d/2}$. We prove the solvability in Sobolev spaces of $Lu=f\in L_{p}$ in bounded $C^{1,1}$-domains, 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 discussed.
