2023

Bindini, Ugo; Rajala, Tapio

We study conditions on closed sets C,F⊂R making the product C×F removable or non-removable for W1,p. The main results show that the Hausdorff-dimension of the smaller dimensional component C determines a critical exponent above which the product is removable for some positive measure sets F, but below which the product is not removable for another collection of positive measure totally disconnected sets F. Moreover, if the set C is Ahlfors-regular, the above removability holds for any totally disconnected F.