论文标题
与均质和不均匀边界条件的差异统像问题
The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions
论文作者
论文摘要
我们考虑$ \ Mathbb {r}^d $中的不规则域上的混合dirichlet--符合问题。将讨论两种类型的规律性结果：$ w^{1，p} $规则性和非区别最大函数估计。假定该域是Reifenberg-flat，并且界面边界是共同限制$ 2 $的Reifenberg-flat，或者本地足够接近$ M $变量的Lipschitz功能，其中$ m = 1，\ ldots，d-2 $。对于非区域最大函数估计，我们还要求域是Lipschitz。
We consider the mixed Dirichlet-conormal problem on irregular domains in $\mathbb{R}^d$. Two types of regularity results will be discussed: the $W^{1,p}$ regularity and a non-tangential maximal function estimate. The domain is assumed to be Reifenberg-flat, and the interfacial boundary is either Reifenberg-flat of co-dimension $2$ or is locally sufficiently close to a Lipschitz function of $m$ variables, where $m=1,\ldots,d-2$. For the non-tangential maximal function estimate, we also require the domain to be Lipschitz.
