Dimension estimates for the boundary of planar Sobolev extension domains

2020/06/25 by Lučić, Danka, Rajala, Tapio, Takanen, Jyrki
#28A75 #46E35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2006.14213

Abstract

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.

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