Dimension estimates for the boundary of planar Sobolev extension domains

preprint2020arXivOpen access

Abstract

We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev W1,pW^{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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Dimension estimates for the boundary of planar Sobolev extension domains | BZPEER