论文标题
平面Sobolev扩展域边界的维度估计值
Dimension estimates for the boundary of planar Sobolev extension domains
论文作者
论文摘要
我们证明了通过边界的弱平均孔隙率通过边界的界面平面Sobolev $ W^{1，P} $扩展域的边界的渐近尺寸上限。示例显示了我们估计的清晰度。
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.
