Characterizating Sobolev Spaces for Arbitrary Open Sets
In this talk I will discuss some recent results obtained in
collaboration with G. Leoni on new characterizations of Sobolev spaces for
arbitrary open sets. The motivation for such a characterization stems from a
2001 paper of Bourgain, Brezis, and Mironescu that gives a related one for
smooth and bounded domains, and an open question on the extension of these
results to arbitrary open sets.