论文标题
线性和完全非线性椭圆方程，带有$ L_ {D} $ - 漂移
Linear and fully nonlinear elliptic equations with $L_{d}$-drift
论文作者
论文摘要
在$ \ Mathbb {r}^{d} $的子域中，我们考虑椭圆形方程$ h \ big（v（x），d v（x），d v（x），d^{2} v（x），x \ big）= 0 $，与$ h $ $ h $ | dv | dv | dv | d $ l y l y life a $ l l y l y lift $ l l l l lift $ y l _ $ l l l y live | dv wime | dv | $ h $对$ x $的依赖性假定为BMO类型。除其他方面，我们证明存在$ d_ {0} \在（d/2，d）$中，因此，对于任何$ p \ in（d_ {0}，d），d）$的方程式具有规定的连续边界数据具有$ w^{2} _ {p，p，text {loc {loc {loc {loc {loc {loc}}的解决方案。即使$ h $是线性的，我们的结果也是新的。
In subdomains of $\mathbb{R}^{d}$ we consider uniformly elliptic equations $H\big(v( x),D v( x),D^{2}v( x), x\big)=0$ with the growth of $H$ with respect to $|Dv|$ controlled by the product of a function from $L_{d}$ times $|Dv|$. The dependence of $H$ on $x$ is assumed to be of BMO type. Among other things we prove that there exists $d_{0}\in(d/2,d)$ such that for any $p\in(d_{0},d)$ the equation with prescribed continuous boundary data has a solution in class $W^{2}_{p,\text{loc}}$. Our results are new even if $H$ is linear.
