Another look at Sobolev spaces

Sunday, 21 January, 2018 - 09:00 - 09:45
LSB 222
Seminar Type: 
Workshop on Fractals and Related Areas
Speaker Name: 
Prof. Ka-Sing LAU
University of Pittsburgh & CUHK

Let Ω be a domain in Rn with smooth boundary, it is well-known that the Sobolev spaces W 1,2(Ω) and W s,2 (Ω); 0 < s < 1 are function spaces that are associated with the Laplacian Δ and the fractional Laplacian (-Δ)s respectively. There are extensions of these concepts to the Besov spaces on certain fractal sets K. In this talk, we will discuss some of the recent developments; in particular we will consider a theorem of Bourgain, Brezis and Mironescu on the limit behavior of W s,2(Ω), s à 1 to W 1,2, and the possible extension of the theorem to Besov spaces on K.