Calculus of Variations and Geometric Measure Theory

D. Lučić - T. Rajala - J. Takanen

Dimension estimates for the boundary of planar Sobolev extension domains

created by lučić on 26 Jun 2020



Inserted: 26 jun 2020

Year: 2020

ArXiv: 2006.14213 PDF


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.