论文标题
平面上能力和Sobolev的双重性
Duality of capacities and Sobolev extendability in the plane
论文作者
论文摘要
我们揭示了能力的双重性与索波列夫妇在平面中的sobolev可扩展性之间的二元性之间的关系，并解释了如何通过容量的双重性读取曲线条件参与Jordan域的sobolev扩展性。最后，作为一个应用程序，我们提供了Jordan Planar域的必要条件的替代证明，为$ W^{1，Q} $ - $ 2 <q <q <\ infty $。
We reveal relations between the duality of capacities and the duality between Sobolev extendability of Jordan domains in the plane, and explain how to read the curve conditions involvd in the Sobolev extendability of Jordan domains via the duality of capacities. Finally as an application, we give an alternative proof of the necessary condition for a Jordan planar domain to be $W^{1, q}$-extension domain when $2 < q < \infty$.
