On Density of Sobolev Functions on Euclidean Domains

Explore recent findings on the density of Sobolev spaces in this 45-minute mathematics lecture. Delve into the relationship between W1,q(Ω) and W1,p(Ω) for domains Ω in Euclidean space, where 1 ≤ p < q ≤ ∞. Examine the removability of measure zero sets for Sobolev functions and investigate extension operators from w1,p(Ω) to W1,p(ℝn). Learn about the collaborative research conducted with P. Koskela and Y. Zhang, presented as part of the Follow-up Workshop to the Junior Hausdorff Trimester Program on Optimal Transportation at the Hausdorff Center for Mathematics.

Tapio Rajala: On density of Sobolev functions on Euclidean domains