论文标题
Carleson扰动规律性问题
Carleson Perturbations for the Regularity Problem
论文作者
论文摘要
我们证明，在Carleson扰动下，$ l^q（\ partialω）$中规则性问题的解决性是稳定的。如果扰动很小，则将可溶性保留在相同的$ l^q $中，并且如果扰动很大，则可以在$ l^{r} $中解决其他$ r \ in（1，\ infty）$中的$ l^{r} $。我们将较早的结果从Kenig和Pipher扩展到非常通用的无界领域，可能具有较低的维度边界，如Guy David和最后两位作者所开发的理论。确切地说，我们只需要域即可访问其AHLFORS常规边界，以及边界上的梯度概念。
We prove that the solvability of the regularity problem in $L^q(\partial Ω)$ is stable under Carleson perturbations. If the perturbation is small, then the solvability is preserved in the same $L^q$, and if the perturbation is large, the regularity problem is solvable in $L^{r}$ for some other $r\in (1,\infty)$. We extend an earlier result from Kenig and Pipher to very general unbounded domains, possibly with lower dimensional boundaries as in the theory developed by Guy David and the last two authors. To be precise, we only need the domain to have non-tangential access to its Ahlfors regular boundary, together with a notion of gradient on the boundary.
