论文标题
关于$ \ overline \ partial $ -solutions的规律性，$ a_q $域，$ c^2 $界限
On regularity of $\overline\partial$-solutions on $a_q$ domains with $C^2$ boundary in complex manifolds
论文作者
论文摘要
我们研究了解决方案的规律性$ u $至$ \ overline \ partial \ partial u = f $在相对紧凑的$ c^2 $ domain $ d $中的复杂流形中，其中$ n $，其中$ f $是$（0，q）$表单。假设在边界$ \ partial d $的每个点上都有$（q+1）$ nage或$（n-q）$阳性levi eigenvalues。在域上存在本地$ l^2 $解决方案的必要条件下，当$ q = 1 $和$ f $时，我们在域关闭域上的解决方案的存在，在Hölder-Zygmund space $λ^r（\ rypline dipline d）中，$ r> r> r> 1 $。对于$ q> 1 $，当$ \ partial d $要么足够光滑，要么是$（n-q）$阳性的levi eigenvalues时，在$ \ partial d $上都可以实现解决方案的规律性。
We study regularity of solutions $u$ to $\overline\partial u=f$ on a relatively compact $C^2$ domain $D$ in a complex manifold of dimension $n$, where $f$ is a $(0,q)$ form. Assume that there are either $(q+1)$ negative or $(n-q)$ positive Levi eigenvalues at each point of boundary $\partial D$. Under the necessary condition that a locally $L^2$ solution exists on the domain, we show the existence of the solutions on the closure of the domain that gain $1/2$ derivative when $q=1$ and $f$ is in the Hölder-Zygmund space $Λ^r(\overline D)$ with $r>1$. For $q>1$, the same regularity for the solutions is achieved when $\partial D$ is either sufficiently smooth or of $(n-q)$ positive Levi eigenvalues everywhere on $\partial D$.
