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.