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math.FA2020
Characterisation of upper gradients on the weighted Euclidean space and applications
Danka Lučić, Enrico Pasqualetto, Tapio Rajala
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and…
math.CA2020
Dimension estimates for the boundary of planar Sobolev extension domains
Danka Lučić, Tapio Rajala, Jyrki Takanen
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev -extension domains via the weak mean porosity of the bou…