# Another look at Sobolev spaces

Date:

Sunday, 21 January, 2018 - 09:00 - 09:45

Venue:

LSB 222

Seminar Type:

Workshop on Fractals and Related Areas

Speaker Name:

Prof. Ka-Sing LAU

Affiliation:

University of Pittsburgh & CUHK

Let Ω be a domain in R* ^{n}* 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*.