Failure of zero extension in parabolic Sobolev spaces

Jongkeun Choi, Doyoon Kim, Kwan Woo

We show that spatial zero extension across the boundary may fail in parabolic Sobolev spaces ${\mathring{\mathcal{H}}}_p^1((0,T)\times \hat{I}\text{c◯})$, which can also be characterized as $$ L_…